Tensor representations of classical locally finite Lie algebras

2007/09/11 by Ivan Penkov, Penkov, I., Konstantin Styrkas +1 · 1 citation
Mathematics · #17B10 #17B20 #17B65 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0709.1525

openalex publication_date 2007/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• Operads, modules over walled Brauer categories, and Koszul complexes

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