Free subalgebras of Lie algebras close to nilpotent

Details Free subalgebras of Lie algebras close to nilpotent Free subalgebras of Lie algebras close to nilpotent

2008-05-06

arxiv.org/abs/0805.0723v2

Groups, Geometry and Dynamics 4 (2010), 15-29

Mathematics

Rings and Algebras

Scientific paper

We prove that for every automata algebra of exponential growth, the associated Lie algebra contains a free subalgebra. For n\geq 1, let L_{n+2} be a Lie algebra with generator set x_1,..., x_{n+2} and the following relations: for k\leq n, any commutator of length $k$ which consists of fewer than k different symbols from {x_1,...,x_{n+2}} is zero. As an application of this result about automata algebras, we prove that for every n\geq 1, L_{n+2} contains a free subalgebra. We also prove the similar result about groups defined by commutator relations.

Affiliated with

Also associated with

No associations

Rating

Free subalgebras of Lie algebras close to nilpotent does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Free subalgebras of Lie algebras close to nilpotent, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Free subalgebras of Lie algebras close to nilpotent will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-209202