Tensor representations of classical locally finite Lie algebras

Abstract

We study the structure of tensor representations of the classical infinite-dimensional locally finite Lie algebras $g{l}_{\infty }$, $s{l}_{\infty }$, $s{p}_{\infty }$ and $s{o}_{\infty }$. In contrast with the finite-dimensional case, these tensor representations are not semisimple. We explicitly describe their Jordan-Holder constituents, socle filtrations, and indecomposable direct summands.

21 pages