Codimension Growth of Strong Lie Nilpotent Associative Algebras |
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Authors: | V M Petrogradsky |
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Institution: | 1. Faculty of Mathematics , Ulyanovsk State University , Ulyanovsk, Russia petrogradsky@rambler.ru |
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Abstract: | We study Lie nilpotent varieties of associative algebras. We explicitly compute the codimension growth for the variety of strong Lie nilpotent associative algebras. The codimension growth is polynomial and found in terms of Stirling numbers of the first kind. To achieve the result we take the free Lie algebra of countable rank L(X), consider its filtration by the lower central series and shift it. Next we apply generating functions of special type to the induced filtration of the universal enveloping algebra U(L(X)) = A(X). |
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Keywords: | Codimension growth Free Lie algebras Lie nilpotence Non-matrix varieties PI algebras Stirling numbers of first kind |
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