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Comparison morphisms between two projective resolutions of monomial algebras

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 نشر من قبل Maria Julia Redondo
 تاريخ النشر 2016
  مجال البحث
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We construct comparison morphisms between two well-known projective resolutions of a monomial algebra $A$: the bar resolution and Bardzells resolution; the first one is used to define the cup product and the Lie bracket on the Hochschild cohomology $HH^*(A)$ and the second one has been shown to be an efficient tool for computations of these cohomology groups. The constructed comparison morphisms allow us to show that the cup product restricted to even degrees of the Hochschild cohomology has a very simple description. Moreover, for $A=k Q/I$ a monomial algebra such that $dim_k e_i A e_j = 1$ whenever there exists an arrow $alpha: i to j in Q_1$, we describe the Lie action of the Lie algebra $HH^1(A)$ on $HH^{ast}(A)$.



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