Tensor representations of classical locally finite Lie algebras

Details Tensor representations of classical locally finite Lie algebras Tensor representations of classical locally finite Lie algebras

2007-09-11

arxiv.org/abs/0709.1525v1

Mathematics

Representation Theory

21 pages

Scientific paper

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.

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