The first cohomology group of the trivial extension of a monomial algebra

Abstract

Given a finite-dimensional monomial algebra A, we consider the trivial extension TA and provide formulae, depending on the characteristic of the field, for the dimensions of the summands HH1(A) and Alt(DA) of the first Hochschild cohomology group HH1(TA). From these a formula for the dimension of HH1(TA) can be derived.