Hochschild cohomology of Beilinson algebra of exterior algebra

CSpace

	Hochschild cohomology of Beilinson algebra of exterior algebra
其他题名	Hochschild cohomology of Beilinson algebra of exterior algebra
	Xu YunGe 1; Zhang Chao 1; Ma XiaoJing 1; Hu QingFeng 1
	2012
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	55 期号:6 页码:1153-1170
摘要	Let I > (n) be the Beilinson algebra of exterior algebra of an n-dimensional vector space, which is derived equivalent to the endomorphism algebra of a tilting complex T = I (i=0) (n) O (X) (i) of coherent O (X) -modules over a projective scheme X = P (k) (n) . In this paper we first construct a minimal projective bimodule resolution of I > (n) , and then apply it to calculate k-dimensions of the Hochschild cohomology groups of I > (n) in terms of parallel paths. Finally, we give an explicit description of the cup product and obtain a Gabriel presentation of Hochschild cohomology ring of I > (n) . As a consequence, we provide a class of algebras of finite global dimension whose Hochschild cohomology rings have non-trivial multiplicative structures.
其他摘要	Let A_n be the Beilinson algebra of exterior algebra of an n-dimensional vector space,which is derived equivalent to the endomorphism algebra End O_X(T) of a tilting complex T = Π_(i=0)~n O_X(i) of coherent O_X-modules over a projective scheme X = P_k~n.In this paper we first construct a minimal projective bimodule resolution of Λ_n,and then apply it to calculate k-dimensions of the Hochschild cohomology groups of Λ_n in terms of parallel paths.Finally,we give an explicit description of the cup product and obtain a Gabriel presentation of Hochschild cohomology ring of Λ_n.As a consequence,we provide a class of algebras of finite global dimension whose Hochschild cohomology rings have non-trivial multiplicative structures.
关键词	REPRESENTATION DIMENSION RESOLUTIONS RING Beilinson algebra finite global dimension Hochschild cohomology ring parallel path
收录类别	CSCD
语种	英语
资助项目	[National Natural Science Foundation of China] ; [Important Foundation of Hubei Provincial Department of Education]
CSCD记录号	CSCD:4598149
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52785
专题	中国科学院数学与系统科学研究院
作者单位	1.湖北大学 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Xu YunGe,Zhang Chao,Ma XiaoJing,et al. Hochschild cohomology of Beilinson algebra of exterior algebra[J]. SCIENCE CHINA-MATHEMATICS,2012,55(6):1153-1170.
APA	Xu YunGe,Zhang Chao,Ma XiaoJing,&Hu QingFeng.(2012).Hochschild cohomology of Beilinson algebra of exterior algebra.SCIENCE CHINA-MATHEMATICS,55(6),1153-1170.
MLA	Xu YunGe,et al."Hochschild cohomology of Beilinson algebra of exterior algebra".SCIENCE CHINA-MATHEMATICS 55.6(2012):1153-1170.