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arXiv · 1112.5492

Graded Embeddings of Finite Dimensional Simple Graded Algebras

Ofir David
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Abstract

Let A,B be finite dimensional G-graded algebras over an algebraically closed field K with char(K)=0, where G is an abelian group, and let Id_G(A) be the set of graded identities of A (res. Id_G(B)). We show that if A,B are G-simple then there is a graded embedding of A in B iff Id_G(B) is contained in Id_G(A). We also give a weaker generalization for the case where A is G-semisimple and B is arbitrary.

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Ofir David. 2012-03-02. Graded Embeddings of Finite Dimensional Simple Graded Algebras. https://doi.org/10.1016/j.jalgebra.2012.06.005

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