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Codimension growth of two-dimensional non-associative algebras


Authors: A. Giambruno, S. Mishchenko and M. Zaicev
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
Published electronically: August 2, 2007
MathSciNet review: 2336552
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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$.


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Additional Information

A. Giambruno
Affiliation: Dipartimento di Matematica e Applicazioni, Via Archirafi 34, 90123 Palermo, Italia
Email: agiambr@unipa.it

S. Mishchenko
Affiliation: Department of Algebra and Geometric Computations, Faculty of Mathematics and Mechanics, Ulyanovsk State University, Ulyanovsk 432700, Russia
Email: mishchenkosp@.ulsu.ru

M. Zaicev
Affiliation: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992 Russia
Email: zaicev@mech.math.msu.su

DOI: https://doi.org/10.1090/S0002-9939-07-08673-X
Keywords: Polynomial identity, codimension growth
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
Article copyright: © Copyright 2007 American Mathematical Society

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