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Constructions of lie algebras and their modules / / George B. Seligman
| Constructions of lie algebras and their modules / / George B. Seligman |
| Autore | Seligman George B. <1927-> |
| Edizione | [1st ed. 1988.] |
| Pubbl/distr/stampa | Berlin, Germany : , : Springer-Verlag, , [1988] |
| Descrizione fisica | 1 online resource (VIII, 196 p.) |
| Disciplina | 512.74 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Modules (Algebra)
Lie algebras Topological groups |
| ISBN | 3-540-38864-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | An introductory example: sl(n,D) -- General considerations -- Involutorial algebras and modules for their skew elements -- Construction of modules with prescribed relative highest weights, for the isotropic algebras of chapter 3 -- Construction of exceptional algebras from quadratic forms -- Representations of exceptional algebras constructed from quadratic forms -- Non-reduced excepticnal algebras with a one-dimensional root space -- Construction of modules for the super-exceptional algebras of rank one -- Complements. |
| Record Nr. | UNISA-996466529903316 |
Seligman George B. <1927->
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| Berlin, Germany : , : Springer-Verlag, , [1988] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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On Lie algebras of prime characteristic / / George B. Seligman
| On Lie algebras of prime characteristic / / George B. Seligman |
| Autore | Seligman George B. <1927-> |
| Pubbl/distr/stampa | Providence, R.I. : , : American Mathematical Society, , 1956 |
| Descrizione fisica | 1 online resource (89 pages) |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Lie algebras |
| ISBN | 0-8218-9960-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""I. DEFINITIONS""; ""II. RESTRICTED LIE ALGEBRAS""; ""III. THE CARTAN DECOMPOSITION""; ""IV. LEMMAS ON REPRESENTATIONS AND THEIR APPLICATIONS""; ""V. WEIGHTS AND ROOTS""; ""VI. SIMPLE SYSTEMS OF ROOTS""; ""VII. EXISTENCE OF SIMPLE SYSTEMS""; ""VIII. SYSTEMS OF TYPE A""; ""IX. SYSTEMS OF TYPE D""; ""X. SYSTEMS OF TYPE B""; ""XI. SYSTEMS OF TYPE C""; ""XII. SYSTEMS OF TYPE G""; ""XIII. SYSTEMS OF TYPE F""; ""XIV. SYSTEMS OF TYPE E""; ""XV. MAXIMAL SIMPLE SYSTEMS""; ""XVI. CLASSIFICATION OF THE SIMPLE ALGEBRAS""; ""XVII. THE CLASSICAL SIMPLE ALGEBRAS""; ""XVIII. THE FIVE EXCEPTIONAL ALGEBRAS""; ""BIBLIOGRAPHY"" |
| Record Nr. | UNINA-9910788767903321 |
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Seligman George B. <1927->
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| Providence, R.I. : , : American Mathematical Society, , 1956 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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On Lie algebras of prime characteristic / / George B. Seligman
| On Lie algebras of prime characteristic / / George B. Seligman |
| Autore | Seligman George B. <1927-> |
| Pubbl/distr/stampa | Providence, R.I. : , : American Mathematical Society, , 1956 |
| Descrizione fisica | 1 online resource (89 pages) |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico | Lie algebras |
| ISBN | 0-8218-9960-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""I. DEFINITIONS""; ""II. RESTRICTED LIE ALGEBRAS""; ""III. THE CARTAN DECOMPOSITION""; ""IV. LEMMAS ON REPRESENTATIONS AND THEIR APPLICATIONS""; ""V. WEIGHTS AND ROOTS""; ""VI. SIMPLE SYSTEMS OF ROOTS""; ""VII. EXISTENCE OF SIMPLE SYSTEMS""; ""VIII. SYSTEMS OF TYPE A""; ""IX. SYSTEMS OF TYPE D""; ""X. SYSTEMS OF TYPE B""; ""XI. SYSTEMS OF TYPE C""; ""XII. SYSTEMS OF TYPE G""; ""XIII. SYSTEMS OF TYPE F""; ""XIV. SYSTEMS OF TYPE E""; ""XV. MAXIMAL SIMPLE SYSTEMS""; ""XVI. CLASSIFICATION OF THE SIMPLE ALGEBRAS""; ""XVII. THE CLASSICAL SIMPLE ALGEBRAS""; ""XVIII. THE FIVE EXCEPTIONAL ALGEBRAS""; ""BIBLIOGRAPHY"" |
| Record Nr. | UNINA-9910818984103321 |
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Seligman George B. <1927->
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||
| Providence, R.I. : , : American Mathematical Society, , 1956 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Rational constructions of modules for simple Lie algebras / / George B. Seligman
| Rational constructions of modules for simple Lie algebras / / George B. Seligman |
| Autore | Seligman George B. <1927-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1981] |
| Descrizione fisica | 1 online resource (203 p.) |
| Disciplina | 512/.55 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Lie algebras
Modules (Algebra) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-7591-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""Foreword""; ""I. Generalities on Finite-Dimensional Modules""; ""Â1. Basic observations on irreducible modules""; ""Â2. Relations in irreducible L-modules""; ""Â3. Induced modules. Construction of irreducible modules.""; ""Â4. A-admissible L0-modules""; ""II. Behavior upon Splitting. Cartan Multiplication""; ""Â1. Modules and field extension""; ""Â2. Cartan multiplication""; ""III. Mappings Satisfying Symmetric Identities""; ""Â1. Solution of the basic recursion""; ""Â2. The canonical example""; ""Â3. A characterization of (Sk (A), Ï?k)""
""Â4. Applications""""IV. Structure of Symmetric Powers""; ""Â1. Summary of classical results; the split case.""; ""Â2. A special minimal ideal in sk(A)""; ""Â3. Symmetric powers for central simple involutorial algebras; the split case.""; ""Â4. The general case""; ""Â5. The minimal ideals of sk(A) are central simple""; ""V. Construction of Representations: Type a and Type C (First Kind)""; ""Â1. The Lie algebras and their fundamental weights""; ""Â2. Construction of representations: Weights of group A""; ""Â3. Weights of group B.""; ""Â4. Weights of group C."" ""Â5. Weights of group D.""""Â6. Weights of groups E and F.""; ""Â7. Summary""; ""VI. Construction of Representations: Type C (Second Kind)""; ""Â1. The Lie algebras and their fundamental weights""; ""Â2. Construction of representations: weights dλj(j > 1)""; ""Â3. Construction of representations: weight kλ1""; ""Â4. Construction of representations: weight kλj + (d-k)λj+l""; ""Â5. Summary""; ""VII. Modules for Lie Algebras of Quadratic Forms.""; ""Â1. The Lie algebras; fundamental weights""; ""Â2. Representations with highest weight λi' i < n"" ""Â3. Representations with highest weight λn""""Â4. Representations of highest weight 2λn·""; ""Â5. Summary. Generating modules""; ""VIII. Exceptional Types I: F4 with Associative Coefficients""; ""Â1. Decomposition of the Lie algebras. Fundamental weights""; ""Â2. Construction of irreducible representations: λl and λ2""; ""Â3. The case D = K: λ3 and λ4""; ""Â4. An embedding of sl(3,Q) in F4(Q)""; ""Â5. Representations of F4(Q): highest weights λ3 , λ4 and combinations""; ""Â6. Summary""; ""IX. Exceptional Types II: Lie Algebras Coordinatized by Octonions"" ""Â1. The algebras sl(3,0) fundamental weights""; ""Â2. The algebras sp(6,0); fundamental weights""; ""Â3. Representations of sl(3,0); the weights 2λ1 , 2λ 2""; ""Â4. Representations of sl(3,0): the weight λl + λ2""; ""Â5. Representations of sl(3,0): 2λ1 + λ2 and λl + 2λ2""; ""Â6. Representations of sl(3,0): 2λ1 + 2λ2 and summary""; ""Â7. An embedding of sl(3,0) in 4p(6,0)""; ""Â8. Fundamental representations for sp(6,0)""; ""Â9. Fundamental representations for F4(0)""; ""X. Exceptional Types III: Relative Type A1"" ""Â1. The Lie algebras sl(2,J) and their fundamental weights"" |
| Record Nr. | UNINA-9910479999303321 |
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Seligman George B. <1927->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1981] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Rational constructions of modules for simple Lie algebras / / George B. Seligman
| Rational constructions of modules for simple Lie algebras / / George B. Seligman |
| Autore | Seligman George B. <1927-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1981] |
| Descrizione fisica | 1 online resource (203 p.) |
| Disciplina | 512/.55 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Lie algebras
Modules (Algebra) |
| ISBN | 0-8218-7591-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Table of Contents -- Foreword -- Part I. Generalities on Finite-Dimensional Modules -- Chapter 1. Basic observations on irreducible modules -- Chapter 2. Relations in irreducible L-modules -- Chapter 3. Induced modules. Construction of irreducible modules. -- Chapter 4. A-admissible L0-modules -- Part II. Behavior upon Splitting. Cartan Multiplication -- Chapter 1. Modules and field extension -- Chapter 2. Cartan multiplication -- Part III. Mappings Satisfying Symmetric Identities -- Chapter 1. Solution of the basic recursion -- Chapter 2. The canonical example -- Chapter 3. A characterization of (Sk (A), Ï?k) -- Chapter 4. Applications -- Part IV. Structure of Symmetric Powers -- Chapter 1. Summary of classical results -- the split case. -- Chapter 2. A special minimal ideal in sk(A) -- Chapter 3. Symmetric powers for central simple involutorial algebras -- the split case. -- Chapter 4. The general case -- Chapter 5. The minimal ideals of sk(A) are central simple -- Part V. Construction of Representations: Type a and Type C (First Kind) -- Chapter 1. The Lie algebras and their fundamental weights -- Chapter 2. Construction of representations: Weights of group A -- Chapter 3. Weights of group B. -- Chapter 4. Weights of group C. -- Chapter 5. Weights of group D. -- Chapter 6. Weights of groups E and F. -- Chapter 7. Summary -- Part VI. Construction of Representations: Type C (Second Kind) -- Chapter 1. The Lie algebras and their fundamental weights -- Chapter 2. Construction of representations: weights dλj(j > 1) -- Chapter 3. Construction of representations: weight kλ1 -- Chapter 4. Construction of representations: weight kλj + (d-k)λj+l -- Chapter 5. Summary -- Part VII. Modules for Lie Algebras of Quadratic Forms. -- Chapter 1. The Lie algebras -- fundamental weights -- Chapter 2. Representations with highest weight λi' i < n -- Chapter 3. Representations with highest weight λn -- Chapter 4. Representations of highest weight 2λn· -- Chapter 5. Summary. Generating modules -- Part VIII. Exceptional Types I: F4 with Associative Coefficients -- Chapter 1. Decomposition of the Lie algebras. Fundamental weights -- Chapter 2. Construction of irreducible representations: λl and λ2 -- Chapter 3. The case D = K: λ3 and λ4 -- Chapter 4. An embedding of sl(3,Q) in F4(Q) -- Chapter 5. Representations of F4(Q): highest weights λ3 , λ4 and combinations -- Chapter 6. Summary -- Part IX. Exceptional Types II: Lie Algebras Coordinatized by Octonions -- Chapter 1. The algebras sl(3,0) fundamental weights -- Chapter 2. The algebras sp(6,0) -- fundamental weights -- Chapter 3. Representations of sl(3,0) -- the weights 2λ1 , 2λ 2 -- Chapter 4. Representations of sl(3,0): the weight λl + λ2 -- Chapter 5. Representations of sl(3,0): 2λ1 + λ2 and λl + 2λ2 -- Chapter 6. Representations of sl(3,0): 2λ1 + 2λ2 and summary -- Chapter 7. An embedding of sl(3,0) in 4p(6,0) -- Chapter 8. Fundamental representations for sp(6,0) -- Chapter 9. Fundamental representations for F4(0) -- Part X. Exceptional Types III: Relative Type A1 -- Chapter 1. The Lie algebras sl(2,J) and their fundamental weights. -- Chapter 2. Fundamental representations for sl(2,J): first identities -- Chapter 3. Second identities -- Chapter 4. Fundamental representations for sl(2,]): general identities -- Chapter 5. Representations of sl(2,J): completeness -- Chapter 6. Remarks on sl(2,C), C a cubic extension -- Part XI. Exceptional Types IV: Relative Type G2. -- Chapter 1. The algebras G2(A) and their fundamental weights -- Chapter 2. An embedding of sl(2,A) in G2(A) -- Chapter 3. Construction of fundamental representations -- Appendices: Splitting Information. |
| Record Nr. | UNINA-9910788779903321 |
|
Seligman George B. <1927->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1981] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Rational constructions of modules for simple Lie algebras / / George B. Seligman
| Rational constructions of modules for simple Lie algebras / / George B. Seligman |
| Autore | Seligman George B. <1927-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1981] |
| Descrizione fisica | 1 online resource (203 p.) |
| Disciplina | 512/.55 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Lie algebras
Modules (Algebra) |
| ISBN | 0-8218-7591-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Table of Contents -- Foreword -- Part I. Generalities on Finite-Dimensional Modules -- Chapter 1. Basic observations on irreducible modules -- Chapter 2. Relations in irreducible L-modules -- Chapter 3. Induced modules. Construction of irreducible modules. -- Chapter 4. A-admissible L0-modules -- Part II. Behavior upon Splitting. Cartan Multiplication -- Chapter 1. Modules and field extension -- Chapter 2. Cartan multiplication -- Part III. Mappings Satisfying Symmetric Identities -- Chapter 1. Solution of the basic recursion -- Chapter 2. The canonical example -- Chapter 3. A characterization of (Sk (A), Ï?k) -- Chapter 4. Applications -- Part IV. Structure of Symmetric Powers -- Chapter 1. Summary of classical results -- the split case. -- Chapter 2. A special minimal ideal in sk(A) -- Chapter 3. Symmetric powers for central simple involutorial algebras -- the split case. -- Chapter 4. The general case -- Chapter 5. The minimal ideals of sk(A) are central simple -- Part V. Construction of Representations: Type a and Type C (First Kind) -- Chapter 1. The Lie algebras and their fundamental weights -- Chapter 2. Construction of representations: Weights of group A -- Chapter 3. Weights of group B. -- Chapter 4. Weights of group C. -- Chapter 5. Weights of group D. -- Chapter 6. Weights of groups E and F. -- Chapter 7. Summary -- Part VI. Construction of Representations: Type C (Second Kind) -- Chapter 1. The Lie algebras and their fundamental weights -- Chapter 2. Construction of representations: weights dλj(j > 1) -- Chapter 3. Construction of representations: weight kλ1 -- Chapter 4. Construction of representations: weight kλj + (d-k)λj+l -- Chapter 5. Summary -- Part VII. Modules for Lie Algebras of Quadratic Forms. -- Chapter 1. The Lie algebras -- fundamental weights -- Chapter 2. Representations with highest weight λi' i < n -- Chapter 3. Representations with highest weight λn -- Chapter 4. Representations of highest weight 2λn· -- Chapter 5. Summary. Generating modules -- Part VIII. Exceptional Types I: F4 with Associative Coefficients -- Chapter 1. Decomposition of the Lie algebras. Fundamental weights -- Chapter 2. Construction of irreducible representations: λl and λ2 -- Chapter 3. The case D = K: λ3 and λ4 -- Chapter 4. An embedding of sl(3,Q) in F4(Q) -- Chapter 5. Representations of F4(Q): highest weights λ3 , λ4 and combinations -- Chapter 6. Summary -- Part IX. Exceptional Types II: Lie Algebras Coordinatized by Octonions -- Chapter 1. The algebras sl(3,0) fundamental weights -- Chapter 2. The algebras sp(6,0) -- fundamental weights -- Chapter 3. Representations of sl(3,0) -- the weights 2λ1 , 2λ 2 -- Chapter 4. Representations of sl(3,0): the weight λl + λ2 -- Chapter 5. Representations of sl(3,0): 2λ1 + λ2 and λl + 2λ2 -- Chapter 6. Representations of sl(3,0): 2λ1 + 2λ2 and summary -- Chapter 7. An embedding of sl(3,0) in 4p(6,0) -- Chapter 8. Fundamental representations for sp(6,0) -- Chapter 9. Fundamental representations for F4(0) -- Part X. Exceptional Types III: Relative Type A1 -- Chapter 1. The Lie algebras sl(2,J) and their fundamental weights. -- Chapter 2. Fundamental representations for sl(2,J): first identities -- Chapter 3. Second identities -- Chapter 4. Fundamental representations for sl(2,]): general identities -- Chapter 5. Representations of sl(2,J): completeness -- Chapter 6. Remarks on sl(2,C), C a cubic extension -- Part XI. Exceptional Types IV: Relative Type G2. -- Chapter 1. The algebras G2(A) and their fundamental weights -- Chapter 2. An embedding of sl(2,A) in G2(A) -- Chapter 3. Construction of fundamental representations -- Appendices: Splitting Information. |
| Record Nr. | UNINA-9910828508103321 |
|
Seligman George B. <1927->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1981] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||