Hochschild cohomology of Beilinson algebra of exterior algebra

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.