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Hochschild homology and cohomology of down-up algebras (1609.09809v1)
Published 30 Sep 2016 in math.KT and math.AG
Abstract: We present a detailed computation of the cyclic and the Hochschild homology and cohomology of generic and 3-Calabi-Yau homogeneous down-up algebras. This family was defined by Benkart and Roby in their study of differential posets. Our calculations are completely explicit, by making use of the Koszul bimodule resolution and arguments similar to those used by the second and third authors for Yang-Mills algebras.