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Identities of graded algebras and codimension growth |
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| Authors: | Yu A Bahturin M V Zaicev |
| Institution: | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1A 5K9 -- and -- Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia ; Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia |
| Abstract: | Let  be a  -graded associative algebra over a field of characteristic zero. In this paper we develop a conjecture that relates the exponent of the growth of polynomial identities of the identity component  to that of the whole of  , in the case where the support of the grading is finite. We prove the conjecture in several natural cases, one of them being the case where  is finite dimensional and  has polynomial growth. |
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