Codimension growth of two-dimensional non-associative algebras
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- by A. Giambruno, S. Mishchenko and M. Zaicev PDF
- Proc. Amer. Math. Soc. 135 (2007), 3405-3415 Request permission
Abstract:
Let $F$ be a field of characteristic zero and let $A$ be a two- dimensional non-associative algebra over $F$. We prove that the sequence $c_n(A), n\!=\!1,2,\ldots ,$ of codimensions of $A$ is either bounded by $n+1$ or grows exponentially as $2^n$. We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is $n+1$, $n\ge 2$.References
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Additional Information
- A. Giambruno
- Affiliation: Dipartimento di Matematica e Applicazioni, Via Archirafi 34, 90123 Palermo, Italia
- MR Author ID: 73185
- ORCID: 0000-0002-3422-2539
- Email: agiambr@unipa.it
- S. Mishchenko
- Affiliation: Department of Algebra and Geometric Computations, Faculty of Mathematics and Mechanics, Ulyanovsk State University, Ulyanovsk 432700, Russia
- MR Author ID: 189236
- Email: mishchenkosp@.ulsu.ru
- M. Zaicev
- Affiliation: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992 Russia
- MR Author ID: 256798
- Email: zaicev@mech.math.msu.su
- Received by editor(s): August 27, 2005
- Received by editor(s) in revised form: February 9, 2006
- Published electronically: August 2, 2007
- Additional Notes: The first author was partially supported by MIUR of Italy; the second author was partially supported by RFFI, grant 01-01-00739 and UR 04.01.036; the third author was partially supported by SSH, grant 1910.2003.1.
- Communicated by: Martin Lorenz
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3405-3415
- MSC (2000): Primary 17A50, 16R10; Secondary 16P90
- DOI: https://doi.org/10.1090/S0002-9939-07-08673-X
- MathSciNet review: 2336552