Let F be a field of characteristic zero and let V be a variety of associative F-algebras graded by a finite abelian group G. If V satisfies an ordinary non-trivial identity, then the sequence cnG(V) of G-codimensions is exponentially bounded. In [2, 3, 8], the authors captured such exponential growth by proving that the limit G(V)=limn→∞cnG(V)nexists and it is an integer, called the G-exponent of 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.

Ioppolo A., Martino F. (2019). Classifying G-graded algebras of exponent two. ISRAEL JOURNAL OF MATHEMATICS, 229(1), 341-356 [10.1007/s11856-018-1804-z].

Classifying G-graded algebras of exponent two

Ioppolo A.
;
Martino F.
2019-01-01

Abstract

Let F be a field of characteristic zero and let V be a variety of associative F-algebras graded by a finite abelian group G. If V satisfies an ordinary non-trivial identity, then the sequence cnG(V) of G-codimensions is exponentially bounded. In [2, 3, 8], the authors captured such exponential growth by proving that the limit G(V)=limn→∞cnG(V)nexists and it is an integer, called the G-exponent of 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.
Settore MAT/02 - Algebra
http://www.springer.com/math/journal/11856
Ioppolo A., Martino F. (2019). Classifying G-graded algebras of exponent two. ISRAEL JOURNAL OF MATHEMATICS, 229(1), 341-356 [10.1007/s11856-018-1804-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/395917
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