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Classifying G-graded algebras of exponent two

Abstract

Let F be a field of characteristic zero and let \(\mathcal{V}\) be a variety of associative F-algebras graded by a finite abelian group G. If \(\mathcal{V}\) satisfies an ordinary non-trivial identity, then the sequence \(c_n^G(\mathcal{V})\) of G-codimensions is exponentially bounded. In [2, 3, 8], the authors captured such exponential growth by proving that the limit \(^G(\mathcal{V}) = {\rm{lim}}_{n \to \infty} \sqrt[n]{{c_n^G(\mathcal{V})}}\) exists and it is an integer, called the G-exponent of \(\mathcal{V}\).

The purpose of this paper is to characterize the varieties of G-graded algebras of exponent greater than 2. As a consequence, we find a characterization for the varieties with exponent equal to 2.

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Correspondence to Antonio Ioppolo.

Additional information

A. Ioppolo was partially supported by GNSAGA-INDAM.

F. Martino was supported by a postdoctoral grant PNPD from Capes, Brazil.

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Ioppolo, A., Martino, F. Classifying G-graded algebras of exponent two. Isr. J. Math. 229, 341–356 (2019). https://doi.org/10.1007/s11856-018-1804-z

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