Symmetric algebras, skew category algebras and inverse semigroups.
An inverse semigroup is a semigroup \(S\) in which for every \(s\) there is a unique \(s^*\) such that \(ss^*s=s\) and \(s^*ss^*=s^*\). A finite dimensional algebra \(A\) over a field \(F\) is called symmetric if \(A\) is isomorphic to \(\Hom_F(A,F)\) as an \(A\)-\(A\)-bimodule. In the paper under review the author uses results from the theory of inverse semigroups to construct some examples of symmetric algebras as skew categories associated to algebras over inverse categories.
scientific article; zbMATH DE number 6155230