Tensor representations of classical locally finite Lie algebras

Penkov, I.; Styrkas, K.

Tensor representations of classical locally finite Lie algebras

Authors

Description

We study the structure of tensor representations of the classical infinite-dimensional locally finite Lie algebras $gl_\infty$, $sl_\infty$, $sp_\infty$ and $so_\infty$. 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