量子外代数的Galois覆盖代数的Hochschild上同调

Hochschild Cohomology of Galois Coverings of Quantum Exterior Algebras

中文关键词:  Hochschild上同调  Galois覆盖  量子外代数.

英文关键词:Hochschild cohomology  Galois covering  quantum exterior algebra.

中文摘要:

      本文研究一类量子代数$\Lambda^n_q$的Hochschild上同调.量子代数$\Lambda^n_q$的极小投射双模分解被构造, $\Lambda^n_q$的各阶Hochschild上同调群的维数被清晰的给出.此外,对一些特殊的情况, $\Lambda^n_q$的上同调环也被清晰的刻画.

英文摘要:

      In this paper, we consider the Hochschild cohomology of a class of quantum algebras $\Lambda_{\mathbbm{q}}^{n}$. We construct a minimal projective bimodule resolution of $\Lambda_{\mathbbm{q}}^{n}$, and calculate the $\k$-dimensions of all the Hochschild cohomology groups of $\Lambda_{\q}^{n}$. Furthermore, we give the Hochschild cohomology ring structure of $\Lambda_{\mathbbm{q}}^{n}$ for some special cases.