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arXiv · 1505.04128

On the Classification of G-Graded Twisted Algebras over Finite Abelian Groups

Juan P. Hernandez·Juan D. Velez·Luis A. Wills-Toro·Edisson Gallego
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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.

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Juan P. Hernandez, Juan D. Velez, Luis A. Wills-Toro, Edisson Gallego. 2015-05-15. On the Classification of G-Graded Twisted Algebras over Finite Abelian Groups. https://arxiv.org/abs/1505.04128

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