Note on the cohomology of color Hopf and Lie algebras
Note on the cohomology of color Hopf and Lie algebras
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DOI：
10.1016/j.jalgebra.2005.11.026
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发表时间：
2005-04
影响因子：
0.9
通讯作者：
Xiao-Wu Chen;Toukaiddine Petit;F. Oystaeyen
中科院分区：
文献类型：
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作者：
Xiao-Wu Chen;Toukaiddine Petit;F. Oystaeyen
设A是具有双射对极的(G，χ)-Hopf代数，M是G-分次A-双模。证明了存在一个同构，其中K通过A的个数被视为平凡的分次A-模，Mad是分次A-双模M的伴随A-模，HHGR-∗表示G-分次Hochschild上同调.作为应用，我们推导出色李代数L的分次上同调与其泛包络代数U(L)的分次Hochschild上同调同构，解决了M.Scheunert的一个问题。
Let A be a (G,χ)-Hopf algebra with bijective antipode and let M be a G-graded A-bimodule. We prove that there exists an isomorphism where K is viewed as the trivial graded A-module via the counit of A, Mad is the adjoint A-module associated to the graded A-bimodule M and HHgr∗denotes the G-graded Hochschild cohomology. As an application, we deduce that the graded cohomology of color Lie algebra L is isomorphic to the graded Hochschild cohomology of its universal enveloping algebra U(L), solving a question of M. Scheunert.