We study the variety of Lie algebras defined by the identity $$ [[x_1,x_2,x_3],\,[x_4,x_5,x_6]]=0 $$ over a field of characteristic zero.
In the case of characteristic zero it is proved that there exist exactly three varieties of linear algebras with the colength equal to one for all degrees.
Oct 22, 2024 · We study the variety of Lie algebras defined by the identity [[x(1), x(2), x(3)], [x(4), x(5), x(6)]] = 0 over a field of characteristic ...
Detailed Record ; Title: On the Colength of a Variety of Lie Algebras. ; Language: English ; Authors: Giambruno, A. · Mishchenko, S. · Zaicev, M. · Ol'Shanskii
It is proved that the colength of every API-variety of Lie algebras grows polynomially, and we give a number of examples in which the colength grows more ...
Asymptotic behaviour of the colength growth functions of varieties of Lie algebras, M V Zaitsev, S P Mishchenko.
Abstract. We study the variety of Lie algebras defined by the identity [Formula: see text] over a field of characteristic zero.
People also ask
What is the concept of Lie algebra?
What is the kernel of the Lie algebra homomorphism?
What are the elements of a Lie in algebra?
What are Lie algebras good for?
We prove that there exist polynilpotent Lie varieties with exponential and overexponential colength growth. We give the exact asymptotics for the colength of a ...
In particular we investigate the colength for the cocharacters of polynilpotent varieties of Lie algebras. We prove that there exist polynilpotent Lie varieties ...
Nov 13, 1997 · The examples show that the growth of colength will be superpolynomial for many important varieties of Lie algebras, such as varieties of ...