Comparison Morphisms and the Hochschild Cohomology Ring of Truncated Quiver Algebras

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...

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

Second Hochschild Cohomology of Convolution Algebras

The Lie Module Structure on the Hochschild Cohomology Groups of Monomial Algebras with Radical Square Zero

We study the Lie module structure given by the Gerstenhaber bracket on the Hochschild cohomology groups of a monomial algebra with radical square zero. The description of such Lie module structure will be given in terms of the combinatorics of the quiver. The Lie module structure will be related to the classification of finite dimensional modules over simple Lie algebras when the quiver is give...

2 00 4 Hochschild ( co ) homology dimension ∗

In 1989 Happel conjectured that for a finite-dimensional algebra A over an algebraically closed field k, gl.dim.A < ∞ if and only if hch.dim.A < ∞. Recently Buchweitz-Green-Madsen-Solberg gave a counterexample to Happel’s conjecture. They found a family of pathological algebra Aq for which gl.dim.Aq = ∞ but hch.dim.Aq = 2. These algebras are pathological in many aspects, however their Hochschil...