Rational constructions of modules for simple Lie algebras / / George B. Seligman

• Record Nr.: UNINA9910788779903321
• Autore: Seligman George B. <1927->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [1981]; ©1981
• ISBN: 0-8218-7591-4
• Descrizione fisica: 1 online resource (203 p.)
• Collana: Contemporary mathematics, ; 5 , 0271-4132
• Disciplina: 512/.55
• Soggetti: Lie algebras; Modules (Algebra)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Bibliography: pages 184-185.
• 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.