LEADER 05486nam 2200541 450 001 9910788779903321 005 20220822061757.0 010 $a0-8218-7591-4 035 $a(CKB)3240000000069530 035 $a(EBL)3113003 035 $a(SSID)ssj0000629418 035 $a(PQKBManifestationID)11369995 035 $a(PQKBTitleCode)TC0000629418 035 $a(PQKBWorkID)10718811 035 $a(PQKB)11075221 035 $a(MiAaPQ)EBC3113003 035 $a(RPAM)2314968 035 $a(PPN)197103235 035 $a(EXLCZ)993240000000069530 100 $a19810820h19811981 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRational constructions of modules for simple Lie algebras /$fGeorge B. Seligman 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[1981] 210 4$d©1981 215 $a1 online resource (203 p.) 225 1 $aContemporary mathematics,$v5$x0271-4132 300 $aDescription based upon print version of record. 311 $a0-8218-5008-3 320 $aBibliography: pages 184-185. 327 $aTable 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), I??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 dI?»j(j > 1) -- Chapter 3. Construction of representations: weight kI?»1 -- Chapter 4. Construction of representations: weight kI?»j + (d-k)I?»j+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 I?»i' i < n -- Chapter 3. Representations with highest weight I?»n -- Chapter 4. Representations of highest weight 2I?»nA?· -- 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: I?»l and I?»2 -- Chapter 3. The case D = K: I?»3 and I?»4 -- Chapter 4. An embedding of sl(3,Q) in F4(Q) -- Chapter 5. Representations of F4(Q): highest weights I?»3 , I?»4 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 2I?»1 , 2I?» 2 -- Chapter 4. Representations of sl(3,0): the weight I?»l + I?»2 -- Chapter 5. Representations of sl(3,0): 2I?»1 + I?»2 and I?»l + 2I?»2 -- Chapter 6. Representations of sl(3,0): 2I?»1 + 2I?»2 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. 410 0$aContemporary mathematics (American Mathematical Society).$v5$x0271-4132 606 $aLie algebras 606 $aModules (Algebra) 615 0$aLie algebras. 615 0$aModules (Algebra) 676 $a512/.55 700 $aSeligman$b George B.$f1927-$042120 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788779903321 996 $aRational Constructions of Modules for Simple Lie Algebras$9382182 997 $aUNINA