Locally finite Lie algebras in positive characteristic

01/28/2014 - 12:15pm
01/28/2014 - 1:10pm
Johanna Hennig (UC San Diego)

For finite dimensional Lie algebras, there is the well-known Ado’s theorem: Every finite dimensional Lie algebra embeds into a finite dimensional associative algebra. Bahturin, Baranov, and Zalesski proved an infinite dimensional version of Ado’s theorem for a simple, locally finite Lie algebra L over a field of characteristic zero: L embeds into a locally finite associative algebra if and only if L is isomorphic to the commutator of skew-symmetric elements of a locally finite, associative algebra with involution. We extend this result to fields of positive characteristic—we provide two structure theorems which reduce to Bahturin, Baranov, Zalesski’s result in characteristic zero and also generalize classical structure theorems for finite dimensional Lie algebras in characteristic p.

Mudd Science Library 126, Pomona College