On the Classification of G-Graded Twisted Algebras over Finite Abelian Groups
Abstract
Let G be a group and let W be an algebra over a field K. We will say that W is a G-graded twisted algebra if W can be written as a direct sum over the elements of G of one dimensional K-vector spaces. It is also assumed that W has no monomial which is a zero divisor. We also demand that W has a multiplicative identity element. We focus in the case where G is a finite abelian group and the field K is either the real numbers or the complex numbers. In this article, using methods of group cohomology, we classify all associative G-graded twisted algebras in the case G is a finite abelian group. On the other hand, by generalizing some of the arguments developed in (Velez et. al., 2014) we present a classification of all G-graded twisted algebras that satisfy certain symmetry condition.
Keywords
Cite
@article{arxiv.1505.04128,
title = {On the Classification of G-Graded Twisted Algebras over Finite Abelian Groups},
author = {Juan P. Hernandez and Juan D. Velez and Luis A. Wills-Toro and Edisson Gallego},
journal= {arXiv preprint arXiv:1505.04128},
year = {2015}
}