Annihilators of simple tensor modules

2012/01/18 by Alexandru-Gabriel Sava, Alexandru Sava, Sava, Alexandru
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1201.3829

28 pages, Master Thesis at Jacobs University Bremen

arxiv created 2012/01/18 · openalex publication_date 2012/01/18 · arxiv updated 2012/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study primitive ideals in the enveloping algebra of finitary locally finite infinite-dimensional complex Lie algebras. In particular we investigate the annihilators of the simple objects in the category of tensor modules. This category has been studied in \citePStyr and \citePS. Moreover we prove that a simple tensor module is completely determined by its annihilator and we introduce a partial order on pairs of Young diagrams that we use to describe the inclusions between the annihilators of the simple tensor modules.

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