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EnglishLet 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.
| Data di pubblicazione: | 2019 |
| Titolo: | Classifying G-graded algebras of exponent two |
| Autori: | |
| Citazione: | Ioppolo, A., & Martino, F. (2019). Classifying G-graded algebras of exponent two. ISRAEL JOURNAL OF MATHEMATICS, 229(1), 341-356. |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s11856-018-1804-z |
| 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. |
| URL: | http://www.springer.com/math/journal/11856 |
| Settore Scientifico Disciplinare: | Settore MAT/02 - Algebra |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/10447/395917
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