Tensor representations of classical locally finite Lie algebras

I. Penkov; K. Styrkas

Tensor representations of classical locally finite Lie algebras

Representation Theory 2007-09-12 v1

Authors: I. Penkov , K. Styrkas

Abstract

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.

Keywords

locally finite lie algebras tensor representations infinite-dimensional lie algebras jordan-holder constituents socle filtrations indecomposable direct summands

Cite

@article{arxiv.0709.1525,
  title  = {Tensor representations of classical locally finite Lie algebras},
  author = {I. Penkov and K. Styrkas},
  journal= {arXiv preprint arXiv:0709.1525},
  year   = {2007}
}

Comments

21 pages

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