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arXiv · 0903.1860

Graded polynomial identities and exponential growth

Eli Aljadeff·Antonio Giambruno·Daniela La Mattina
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Abstract

Let A be a finite dimensional algebra over a field of characteristic zero graded by a finite abelian group G. Here we study a growth function related to the graded polynomial identities satisfied by A by computing the exponential rate of growth of the sequence of graded codimensions of A. We prove that the G-exponent of A exists and is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of A.

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Eli Aljadeff, Antonio Giambruno, Daniela La Mattina. 2009-03-10. Graded polynomial identities and exponential growth. https://arxiv.org/abs/0903.1860

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