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-modul...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.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10971206 and 11171325)Important Foundation of Hubei Provincial Department of Education (Grant No.D20101003)
文摘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.
