Comparison morphisms between two projective resolutions of monomial algebras

ROMAN, LUCRECIA; REDONDO, MARIA JULIA

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahia Blanca; Año: 2018 vol. 59 p. 1 - 31

0041-6932

We construct comparison morphisms between two well-known projective resolu-tions of a monomial algebra A: the bar resolution BarA and Bardzell?s resolution ApA;the first one is used to define the cup product and the Lie bracket on the Hochschildcohomology HH∗(A) and the second one has been shown to be an efficient tool forcomputations of these cohomology groups. The constructed comparison morphismsallow us to show that the cup product restricted to even degrees of the Hochschildcohomology has a very simple description. Moreover, if A = kQ/I is a monomialalgebra such that dimk eiAej = 1 whenever there exists an arrow α : i → j ∈ Q1, wedescribe the Lie action of the Lie algebra HH1(A) on HH∗(A).