The purpose of this article is to prescnt by using vector space methods. a formula as how to calculate the covariance of the outer product of two independent random vecters in inter product space and to makes a discus...The purpose of this article is to prescnt by using vector space methods. a formula as how to calculate the covariance of the outer product of two independent random vecters in inter product space and to makes a discussion on the covariance of the orthogonally invariant random vector and that of the weakly spherically distributed orter produt.展开更多
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
文摘The purpose of this article is to prescnt by using vector space methods. a formula as how to calculate the covariance of the outer product of two independent random vecters in inter product space and to makes a discussion on the covariance of the orthogonally invariant random vector and that of the weakly spherically distributed orter produt.
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.
