Title: Symmetric algebras, skew category algebras and inverse semigroups;

Autor: C.C. Todea;   

Address: Department of Mathematics, Technical University of Cluj-Napoca, Str. G. Baritiu 25,
 Cluj-Napoca 400027, Romania;

Abstract: 

We use results from the theory of inverse semigroups to identify and define a class of symmetric algebras, which we call inverse-symmetric algebras. 
For a finite inverse category $\mathcal{C}$ we define the skew category algebra associated to a $\mathcal{C}$-algebra, which satisfies some additional 
properties, and we prove that remains inverse-symmetric. The classical examples of symmetric algebras: matrix algebra, Iwahori-Hecke algebra and the 
(twisted) group algebra are inverse-symmetric.


Status: published/2012.