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 | References | Similar Articles | Additional Information

Abstract: Let be a field of characteristic zero and let be a two- dimensional non-associative algebra over . We prove that the sequence of codimensions of is either bounded by or grows exponentially as . 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 , .

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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