Poisson and Hochschild cohomology and the semiclassical limit
Poisson and Hochschild cohomology and the semiclassical limit
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DOI：
10.4171/jncg/204
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发表时间：
2013-04
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--
通讯作者：
M. Towers
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文献类型：
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作者：
M. Towers
设B是具有半经典极限A的量子代数.证明了在一定的假设下，$B^e$可以看作是$A$的Poisson包络代数的变形，并给出了当$B$是Koszul时，$B$的Hochschild上同调是$A$的Poisson上同调的变形的一个判据.证明了2 × 2量子矩阵代数的条件，并计算了其半经典极限的Hochschild上同调和Poisson上同调.
Let $B$ be a quantum algebra possessing a semiclassical limit $A$. We show that under certain hypotheses $B^e$ can be thought of as a deformation of the Poisson enveloping algebra of $A$, and we give a criterion for the Hochschild cohomology of $B$ to be a deformation of the Poisson cohomology of $A$ in the case that $B$ is Koszul. We verify that condition for the algebra of $2\times 2$ quantum matrices and calculate its Hochschild cohomology and the Poisson cohomology of its semiclassical limit.