A generalisation of the category $\mathcal{O}$ of Bernstein-Bernstein-Gelfand
Guillaume Tomasini (IRMA)
TL;DR
This paper introduces a new family of categories generalizing the Bernstein-Gelfand-Gelfand category for reductive Lie algebras, classifies simple modules, and establishes semisimplicity results.
Contribution
It extends the classical category to a broader family for reductive Lie algebras, providing new classification and semisimplicity insights.
Findings
Classified simple modules for some generalized categories
Proved semisimplicity in certain cases
Extended the framework of category
Abstract
Given a reductive Lie algebra over the complex numbers, we introduce a family of category which generalises the BGG category . We also classify the simple modules for some of these categories and prove a semisimplicity result.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra