A Lie algebra ╟ is called locally finite dimensional or simply locally finite if every finite dimensional subset of ╟ is contained or equivalently generates a finite dimensional subalgebra of ╟. Note that a Lie algebra is locally finite if and only if it is the directed union of its finite dimensional subalgebras.
N. Stumme, The Structure of Locally Finite Split Lie Algebras, Ph.D. thesis, Darmstadt University of Technology, 1999.
A simple algebra of the third or fourth type "splits" any locally finite variety that contains it (Exercise 14.9(1)).
PDF | On Jan 4, 2001, K.-H. Neeb and others published The classification of locally finite split simple Lie algebras | Find, read and cite all the research ...
Article The classification of locally finite split simple Lie algebras was published on April 4, 2001 in the journal Journal für die reine und angewandte ...
The author studies the structure of locally finite Lie algebras over fields of characteristic zero that have a weight space decomposition with respect to a ...
May 24, 2020 · In the present paper we study local and 2-local derivations of locally finite split simple Lie algebras. Namely, we show that every local and 2- ...
Abstract. We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We ...
Jul 22, 2016 · An algebra in which every subalgebra with finitely many generators has finite dimension over the ground field.
They fall into four distinct families of isomorphism classes, parametrised by the locally finite root systems of type AJ , BJ , CJ and DJ (see. [LN04]). On the ...