# Tensor representations of classical locally finite Lie algebras - Mathematics > Representation Theory

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Abstract: We study the structure of tensor representations of the classicalinfinite-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 theirJordan-Holder constituents, socle filtrations, and indecomposable directsummands.

Autor: I. Penkov, K. Styrkas

Fuente: https://arxiv.org/