2015/10/09 by Yuri Bahturin, Bahturin, Yuri, Diogo Diniz Pereira da Silva e Silva +1
Computer Science · Mathematics · #16K20 #16R10 #16W50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1510.02832
openalex publication_date 2015/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.