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Seligman G.B. — Constructions of Lie Algebras and Their Modules
Seligman G.B. — Constructions of Lie Algebras and Their Modules

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Название: Constructions of Lie Algebras and Their Modules

Автор: Seligman G.B.

Аннотация:

This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 190

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A_k(V)$ = k-th even Clifford algebra      27
$\lambda$-admissible modules      3 24 39 50
Absolutely irreducible modules      181
Allison algebras      121 136
Allison algebras from non-simple cubic Jordan algebras      136
Allison-Faulkner constructions      140
Benkart’s coordinatizations      180
Cartan multiplication      4 19 38
Clifford algebra      52
Constructions of exceptional Jordan division algebras (Tits)      179
Division Allison algebra      125
Exceptional Lie algebras of relative, rank 1, type $E_6$,      79 87 105
Exceptional Lie algebras of relative, rank 1, type $E_7$,      82 88 103
Exceptional Lie algebras of relative, rank 1, type $E_8$      77 86 101
Exceptional Lie algebras of relative, rank 1, type $F_4$,      77 85 86 99
Exceptional Lie algebras of relative, rank 2, type $E_6$      73 90 107
Exceptional Lie algebras of relative, rank 2, type $E_7$      75 89 108
Exceptional Lie algebras of relative, rank 2, type $E_8$      69 91 110
Forms, hermitian and anti-hermitian      21
Freudenthal triple systems      115
Fundamental weights      50 92
Galois-theoretic methods      181—183
Highest weight spaces      2
Homogeneous case of Allison algebras from special Jordan algebras      147 154
Ideals in symmetric powers (Saltman)      11
Involution      21
Involution in Clifford algebra      53
Involution of first/second kinds      21
Involution of orthogonal/symplectic type      21
Irreducible modules for classical algebras, algebras of inner type A      9
Irreducible modules for classical algebras, algebras of outer type A      35
Irreducible modules for classical algebras, algebras of type B      36
Irreducible modules for classical algebras, algebras of type C      33
Irreducible modules for classical algebras, algebras of type D      34 36 172
Kantor algebras      115 121
Koecher — Tits construction      179
McCrimmon’s theorem on cubic composition algebras      127 128
Minimum condition on inner Ideals      180
Modules for [AA], A central simple      9
Non-homogeneous case of Allison algebras from special Jordan algebras      152 154
Pflster’s examples of quadratic forms      97 98
Quadratic forms giving rise to exceptional algebras      96—98
Rationality of all irreducible modules      184 185
Reductive dual pairs      83
Sl(n,D)      1
Special cubic Jordan algebras and associated Allison algebras      137 144
Splitting, Allison algebras      157 ff
Splitting, exceptional algebras from quadratic forms      85 ff
Splitting, involutorial algebras      29 ff
Splitting, irreducible modules      19
Splitting, ordering of roots      18
Splitting, Sl(l,A)      6
Splitting, super-exceptional Lie algebras      159 ff
Strongly degenerate Lie algebras      180
Super-exceptional rank 1 algebras      141
Super-exceptional rank 1 algebras, Non-existence of $F_4$’s      151 166
Super-exceptional rank 1 algebras, type $E_6$      161—162
Super-exceptional rank 1 algebras, type $E_7$      162—164
Super-exceptional rank 1 algebras, type $E_8$      164—166
Super-exceptional rank 1 algebras, type D      159—-160
Symmetric identities      5
Symmetric powers      5
System of roots of algebra of skew elements      22 23
Tensor products of spin and tensor modules      60
Tensor products of spin modules      58
Test-triples      63
Trilinear identities for Sl(2)-modules      117—118
Trilinear identities for spin modules      63—65
Triple tensor products of Sl(2)-modules      116
Zelmanov’s theorem      181
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