Happel问题和Snashall-Solberg猜想  

On Happel's Question and Snashall-Solberg's Conjecture

作　　者：徐运阁[1] 章超[2] 

机构地区：[1]湖北大学数学与计算机科学学院,武汉430062 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《数学学报（中文版）》2012年第6期1067-1084,共18页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10971206;11171325)

摘　　要：众所周知,有限维代数的Hochschild(上)同调群与它的整体维数以及支撑簇(support variety)理论密切相关.本文考虑了几类Koszul代数的Hochschild上同调,为Happel问题和Snashall-Solberg猜想提供了更多的反例,而且覆盖了很多已知的反例.特别地,我们证明了二元量子外代数A_q的一类Z_n×Z_n-Galois覆盖代数为Happel问题提供了反例,同时,代数A_q的一类Z_n和Z_n×Z_m-Galois覆盖代数的单点余扩张提供了Snashall-Solberg猜想的反例.It is well known that the Hochschild（co） homology of a finite dimensional algebra is closely related to its global dimension and the support variety.In this paper we consider the Hochschild cohomology of some classes of Koszul algebras.As a consequence, we provide more counterexamples to Happel＇s question and Snashall-Solberg＇s conjecture which generalize many counterexamples to these conjectures studied in the literature.In particular,we show that a family of Z_n x Z_n-Galois covering algebras of quantized exterior algebra A_q in two variables answer negatively to Happel＇s question, and meanwhile,the one-point coextensions of Z_n and Z_n×Z_m-Galois covering algebras of A_q negate the Snashal.-Solberg＇s conjecture.

关 键 词：Hochschild上同调环 Happel问题 Snashall-Solberg猜想 Koszul对偶 

分 类 号：O181[理学—数学]