A new type of diagrams for modules
Stephanos Gekas

TL;DR
This paper introduces a novel diagram type called the 'central tuned diagram' for finitely generated modules, utilizing the concept of 'the virtual category,' with applications in modular representations of finite groups of Lie type.
Contribution
It presents the existence proof of the 'central tuned diagram' and introduces the idea of 'the virtual category' for modules, advancing module diagram theory.
Findings
Existence of the 'central tuned diagram' for certain modules.
Introduction of 'the virtual category' concept.
Potential applications in modular representation theory.
Abstract
We introduce a new type of diagrams and prove the existence of a particular one, the "central tuned diagram", with some optimal features, for finitely generated modules of certain categories. This is achieved by getting to the idea of "the virtual category" of a module. Important applications are specifically suggested to the modular representations of finite groups of Lie type.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras
