Graded identities of simple real graded division algebras

Let A and B be finite dimensional simple real algebras with division gradings by an abelian group G. In this paper we give necessary and sufficient conditions for the coincidence of the graded identities of A and B. We also prove that every finite dimensional simple real algebra with a G-grading sat...

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Bibliographic Details
Published in:arXiv.org 2016-02
Main Authors: Bahturin, Yuri, Diogo Diniz Pereira da Silva e Silva
Format: Article
Language:English
Subjects:
Algebra
Fields (mathematics)
Grading
Group theory
Mathematical analysis
Matrix algebra
Online Access:Get full text
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Summary:Let A and B be finite dimensional simple real algebras with division gradings by an abelian group G. In this paper we give necessary and sufficient conditions for the coincidence of the graded identities of A and B. We also prove that every finite dimensional simple real algebra with a G-grading satisfies the same graded identities as a matrix algebra over an algebra D with a division grading that is either a regular grading or a non-regular Pauli grading. Moreover we determine when the graded identities of two such algebras coincide. For graded simple algebras over an algebraically closed field it is known that two algebras satisfy the same graded identities if and only if they are isomorphic as graded algebras.
ISSN:2331-8422