an:05358188
Zbl 1184.17003
Mishchenko, S. P.; Cherevatenko, O. I.
Necessary and sufficient conditions for a variety of Leibniz algebras to have polynomial growth
EN
J. Math. Sci., New York 152, No. 2, 282-287 (2008); translation from Fundam. Prikl. Mat. 12, No. 8, 207-215 (2006).
00231990
2008
j
17A32
codimension sequence of polynomial identities of Leibniz algebras
Summary: 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
\[
N_2 A,\widetilde{V_1 } \not\subset V \subset \widetilde{N_c A}
\]
holds, where \(N_2A\) is the variety of Lie algebras defined by the identity \((x_1 x_2)(x_3 x_4)(x_5 x_6)\equiv 0,\widetilde{V_1}\) is the variety of Leibniz algebras defined by the identity \(x_1(x_2 x_3)(x_4 x_5)\equiv 0\), and \(\widetilde{N_cA}\) is the variety of Leibniz algebras defined by the identity \((x_1 x_2)(x_{2c+1}x_{2c+2})\equiv 0\).