Alexander Baranov

Diagonal direct limits of simple lie algebras

The aim of this article is to classify diagonal locally simple Lie algebras of countable dimension over an algebraically closed field of zero characteristic. We also give some remarks on classification of locally simple associative algebras. Recall that an algebra A is called locally finite if any finite subset of A is contained in a finite-dimensional subalgebra. If these subalgebras can be chosen simple, A is called locally simple. Observe that A is simple in this case. Let F be an algebraically closed field of zero characteristic, A be a locally simple associative algebra of countable dimension over F . It follows from the definition that there is an increasing sequence of simple subalgebras M1 ⊂ M2 ⊂M3 ⊂ . . . of A such that A = ∪i=1Mi. It is more convenient to write M1 →M2 →M3 → . . . (1)

Finitary Lie algebras

Abstract An algebra is called finitary if it consists of finite-rank transformations of a vector space. We classify finitary simple and finitary irreducible Lie algebras over an algebraically closed field of characteristic ≠2,3.

Simple Diagonal Locally Finite Lie Algebras

The ground field

Branching Rules for Modular Fundamental Representations of Symplectic Groups

F

Plain Representations of Lie Algebras

is an algebraically closed field of zero characteristic, and

Classification of the direct limits of involution simple associative algebras and the corresponding dimension groups

{\Bbb N}

MINIMAL INDUCTIVE SYSTEMS OF MODULAR REPRESENTATIONS FOR NATURALLY EMBEDDED ALGEBRAIC AND FINITE GROUPS OF TYPE A

is the set of natural numbers. Let

MODULAR BRANCHING RULES FOR 2-COLUMN DIAGRAM REPRESENTATIONS OF GENERAL LINEAR GROUPS

L

Infinite dimensional irreducible Lie algebras containing transformations of finite rank

be a locally finite-dimensional (or {\em locally finite}, for brevity) Lie algebra. Assume for simplicity that

Wedderburn-Malcev decomposition of one-sided ideals of finite dimensional algebras

L