On special covariants in the exterior algebra of a simple Lie algebra

被引：5

作者：

De Concini, Corrado ^{[1
]}

Frajria, Pierluigi Moesneder ^{[2
]}

Papi, Paolo ^{[1
]}

Procesi, Claudio ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[2] Politecn Milan, Polo Reg Como, I-22100 Como, Italy

来源：

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2014年 / 25卷 / 03期

关键词：

Exterior algebra; invariants; little adjoint representation; small representation; THEOREM;

D O I：

10.4171/RLM/682

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the n-th symmetric power of the defining representation. As main result we prove that this subspace is a free module over the subalgebra of the exterior algebra generated by all primitive invariants except the one of highest degree.

引用

页码：331 / 344

页数：14

共 50 条

[31] The Lie Lie algebra
Conant, Jim
QUANTUM TOPOLOGY, 2017, 8 (04) : 667 - 714
[32] Hochschild cohomology of Beilinson algebra of exterior algebra
Xu YunGe
Zhang Chao
Ma XiaoJing
Hu QingFeng
SCIENCE CHINA-MATHEMATICS, 2012, 55 (06) : 1153 - 1170
[33] Hochschild cohomology of Beilinson algebra of exterior algebra
YunGe Xu
Chao Zhang
XiaoJing Ma
QingFeng Hu
Science China Mathematics, 2012, 55 : 1153 - 1170
[34] Hochschild cohomology of Beilinson algebra of exterior algebra
XU YunGe 1
2 Academy of Mathematics and System Science
ScienceChina(Mathematics), 2012, 55 (06) : 1153 - 1170
[35] Leibniz algebra deformations of a Lie algebra
Fialowski, Alice
Mandal, Ashis
JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (09)
[36] ENVELOPING ALGEBRA OF RESOLUBLE LIE ALGEBRA
CONZE, N
DUFLO, M
BULLETIN DES SCIENCES MATHEMATIQUES, 1970, 94 (03): : 201 - &
[37] LIE ALGEBRA EXTENSIONS OF POINCARE ALGEBRA
GALINDO, A
JOURNAL OF MATHEMATICAL PHYSICS, 1967, 8 (04) : 768 - &
[38] Recoupling Lie algebra and universal ω-algebra
Joyce, WP
JOURNAL OF MATHEMATICAL PHYSICS, 2004, 45 (10) : 3859 - 3877
[39] CENTER OF ENVELOPE ALGEBRA OF A LIE ALGEBRA
DIXMIER, J
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1967, 265 (15): : 408 - &
[40] DERIVATIONS OF THE LIE-ALGEBRA STRUCTURE OF THE ENVELOPING ALGEBRA OF A SEMISIMPLE LIE-ALGEBRA
DEWILDE, M
JASON, A
MUKILA, PMW
TOUSSET, E
VANHAUTEN, F
COCAIKO, J
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 320 (11): : 1299 - 1304

← 1 2 3 4 5 →