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In this paper we define almost gentle algebras. They are monomial specialmultiserial algebras generalizing gentle algebras. We show that the trivialextension of an almost gentle algebra by its minimal injective co-generator isa symmetric special multiserial algebra and hence a Brauer configurationalgebra. Conversely, we show that any almost gentle algebra is an admissiblecut of a unique Brauer configuration algebra and as a consequence, we obtainthat every Brauer configuration algebra with multiplicity function identicallyone, is the trivial extension of an almost gentle algebra. We show that toevery almost gentle algebra A is associated a hypergraph, and that thishypergraph induces the Brauer configuration of the trivial extension of A.Amongst other things, this gives a combinatorial criterion to decide when twoalmost gentle algebras have isomorphic trivial extensions.

Almost gentle algebras and their trivial extensions