Hochschild cohomology related to graded down-up algebras with weights (1,n)

Abstract

Let [Formula: see text] be a graded down-up algebra with [Formula: see text] and [Formula: see text], and let [Formula: see text] be the Beilinson algebra of [Formula: see text]. If [Formula: see text], then a description of the Hochschild cohomology group of [Formula: see text] is known. In this paper, we calculate the Hochschild cohomology group of [Formula: see text] for the case [Formula: see text]. As an application, we see that the structure of the bounded derived category of the noncommutative projective scheme of [Formula: see text] is different depending on whether (10) [Formula: see text] [Formula: see text] is zero or not. Moreover, it turns out that there is a difference between the cases [Formula: see text] and [Formula: see text] in the context of Grothendieck groups.