A Class of Finite-dimensional Lie Superalgebras of Hamiltonian Type

被引：5

作者：

Ren, Li ^{[1
]}

Mu, Qiang ^{[2
]}

Zhang, Yongzheng ^{[1
]}

机构：

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Harbin Normal Univ, Sch Math, Harbin 150080, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2011年 / 18卷 / 02期

基金：

中国国家自然科学基金;

关键词：

derivation superalgebra; restricted Lie superalgebra; CARTAN-TYPE; ALGEBRAS; CLASSIFICATION;

D O I：

10.1142/S1005386711000241

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A class of finite-dimensional Cartan-type Lie superalgebras H(n, m) over a field of prime characteristic is studied in this paper. We first determine the derivation superalgebra of H(n, m). Then we obtain that H(n, m) is restrictable and it is an extension of the Lie superalgebra (H) over tilde (n). Finally, we prove that H(n, m) is isomorphic to a subalgebra of the restricted Hamiltonian Lie superalgebra H(n, m, (1) under bar).

引用

页码：347 / 360

页数：14

共 50 条

[31] A class of generalized odd Hamiltonian Lie superalgebras
Li Ren
Qiang Mu
Yongzheng Zhang
Frontiers of Mathematics in China, 2014, 9 : 1105 - 1129
[32] Infinite-dimensional Hamiltonian Lie superalgebras
Qiang Mu
YongZheng Zhang
Science China Mathematics, 2010, 53 : 1625 - 1634
[33] Finite-dimensional representations of map superalgebras
Calixto, Lucas
Macedo, Tiago
LINEAR ALGEBRA AND ITS APPLICATIONS, 2023, 676 : 104 - 130
[34] Infinite-dimensional Hamiltonian Lie superalgebras
Mu Qiang
Zhang YongZheng
SCIENCE CHINA-MATHEMATICS, 2010, 53 (06) : 1625 - 1634
[35] Infinite-dimensional Hamiltonian Lie superalgebras
MU Qiang1
2School of Mathematics
Science China(Mathematics), 2010, 53 (06) : 1625 - 1634
[36] Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs
Gorelik, Maria
Kac, Victor G.
Frajria, Pierluigi Moeseneder
Papi, Paolo
JAPANESE JOURNAL OF MATHEMATICS, 2012, 7 (01): : 41 - 134
[37] IRREDUCIBLE FINITE-DIMENSIONAL REPRESENTATIONS OF LIE-SUPERALGEBRAS GELFAND-TSETLIN BASIS
PALEV, CD
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1987, 21 (03) : 245 - 246
[38] Finite-Dimensional Half-Integer Weight Modules over Queer Lie Superalgebras
Shun-Jen Cheng
Jae-Hoon Kwon
Communications in Mathematical Physics, 2016, 346 : 945 - 965
[39] On Complete Integrability of a Large Class of Finite-dimensional Hamiltonian Systems
屠规彰
数学进展, 1991, (01) : 60 - 74
[40] Restricted Representations of Lie Superalgebras of Hamiltonian Type
Yu-Feng Yao
Bin Shu
Algebras and Representation Theory, 2013, 16 : 615 - 632

← 1 2 3 4 5 →