Necessary and sufficient conditions for a variety of Leibniz algebras to have polynomial growth

被引：0
作者：
Mishchenko S.P. [1 ]
Cherevatenko O.I. [2 ]
机构：
[1] Ulyanovsk State University, Ulyanovsk
[2] Ulyanovsk Pedagogical State University, Ulyanovsk
来源：
Journal of Mathematical Sciences | 2008年 / 152卷 / 2期
基金：
俄罗斯基础研究基金会;
关键词：
Inductive Hypothesis; Variety Versus; Young Diagram; Polynomial Growth; Free Algebra;
D O I：
10.1007/s10958-008-9054-y
中图分类号：
学科分类号：
摘要：
We study the behavior of the codimension sequence of polynomial identities of Leibniz algebras over a field of characteristic 0. We prove that a variety V has polynomial growth if and only if the condition N2A, V with combining double tilde1 ⊄ V ⊂ N with combining double tildecA holds, where N2A is the variety of Lie algebras defined by the identity (x1x2) (x3x 4)(x5x6) ≡ 0, V with combining double tilde1 is the variety of Leibniz algebras defined by the identity x1(x2x3)(x4x5) ≡ 0, and N with combining double tildecA is the variety of Leibniz algebras defined by the identity (x1x2) ⋯ (x 2c+1x2c+2) ≡ 0. © 2008 Springer Science+Business Media, Inc.
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页码：282 / 287
页数：5
相关论文
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