Cohomology of Lie superalgebras and their generalizations
Cohomology of Lie superalgebras and their generalizations
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DOI：
10.1063/1.532508
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发表时间：
1997-01
影响因子：
1.3
通讯作者：
M. Scheunert;R. Zhang
中科院分区：
文献类型：
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作者：
M. Scheunert;R. Zhang
李超代数的上同调群，更一般地说，e李代数，介绍和研究。主要强调的是在模的系数是非平凡的情况下。证明了两个一般性命题，这有助于计算上同调群。包括几个例子，以显示超级情况的特点。对于L=sl（1| 2）中，确定了有限维单分次L-模的上同调群H1（L，V）和H2（L，V），并证明了H2（L，U（L））[其中U（L）是L的包络代数]是平凡的.这意味着超代数U（L）不允许任何非平凡的形式变形（在Gerstenhaber意义下）。将加兰的李代数泛中心扩张理论推广到e-李代数的情形.
The cohomology groups of Lie superalgebras and, more generally, of e Lie algebras, are introduced and investigated. The main emphasis is on the case where the module of coefficients is nontrivial. Two general propositions are proved, which help to calculate the cohomology groups. Several examples are included to show the peculiarities of the super case. For L=sl(1|2), the cohomology groups H1(L,V) and H2(L,V), with V a finite-dimensional simple graded L-module, are determined, and the result is used to show that H2(L,U(L)) [with U(L) the enveloping algebra of L] is trivial. This implies that the superalgebra U(L) does not admit any nontrivial formal deformations (in the sense of Gerstenhaber). Garland’s theory of universal central extensions of Lie algebras is generalized to the case of e Lie algebras.