Hochschild cohomology of Beilinson algebra of exterior algebra

Let An be the Beilinson algebra of exterior algebra of an n-dimensional vector space, which is derived equivalent to the endomorphism algebra Endox （T） of a tilting complex T = II^ni=0^Ox （i） of coherent COx-modules over a projective scheme X = P^nk. In this paper we first construct a minimal projec...

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Bibliographic Details
Published in:Science China. Mathematics 2012-06, Vol.55 (6), p.1153-1170
Main Authors: Xu, YunGe, Zhang, Chao, Ma, XiaoJing, Hu, QingFeng
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
China
Coherence
Equivalence
Exteriors
Hochschild
Mathematical analysis
Mathematics
Mathematics and Statistics
n维向量空间
Rings (mathematics)
Vector spaces
上同调群
同调代数
外代数
并行路径
松
自同态
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Summary:Let An be the Beilinson algebra of exterior algebra of an n-dimensional vector space, which is derived equivalent to the endomorphism algebra Endox （T） of a tilting complex T = II^ni=0^Ox （i） of coherent COx-modules over a projective scheme X = P^nk. In this paper we first construct a minimal projective bimodule resolution of An, and then apply it to calculate k-dimensions of the Hochsehild cohomology groups of An 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 An. As a consequence, we provide a class of algebras of finite global dimension whose Hochschild cohomology rings have non-trivial multiplicative structures.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-012-4388-9