Hochschild cohomology of truncated quiver algebras

2 00 5 Hochschild cohomology of truncated quiver algebras ∗

For a truncated quiver algebra over a field of arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles. MSC(2000): 16E40, 16E10, 16G10

The Cohomology Ring of Truncated Quiver Algebras

In this paper we determine the ring structure of the Hochschild cohomology of truncated quiver algebras with the Yoneda product. On the one hand Locateli described the cohomology groups in terms of classes of pairs of paths using minimal resolutions. On the other hand, the Yoneda product has a nice description on the bar resolution as the usual cup product. Our first main result is the explicit...

Comparison Morphisms and the Hochschild Cohomology Ring of Truncated Quiver Algebras

A main contribution of this paper is the explicit construction of comparison morphisms between the standard bar resolution and Bardzell’s minimal resolution for truncated quiver algebras (TQA’s). As a direct application we describe explicitely the Yoneda product and derive several results on the structure of the cohomology ring of TQA’s. For instance, we show that the product of odd degree coho...

Second Hochschild Cohomology of Convolution Algebras

Hochschild Cohomology of Truncated Polynomials

The main result of this paper is to calculate the Batalin-Vilkovisky structure of HH∗(C∗(KPn;R);C∗(KPn;R)) for K = C andH, and R = Z and any field; and shows that in the special case when M = CP 1 = S2, and R = Z, this structure can not be identified with the BV-structure of H∗(LS 2;Z) computed by Luc Memichi in [16]. However, the induced Gerstenhaber structures are still identified in this cas...