Homological stability and Graham-Lehrer cellular algebras
Guy Boyde
TL;DR
This paper connects recent homological stability results of algebras with Graham-Lehrer cellular algebra theory, bridging topology and representation theory to deepen understanding of algebraic structures.
Contribution
It reformulates homological stability results within the framework of cellular algebras, linking topology and representation theory.
Findings
Homological stability results are expressed in cellular algebra language
Establishes connections between topological and algebraic perspectives
Lays groundwork for further interdisciplinary research
Abstract
We show how to formulate some recent results from homological stability of algebras in Graham and Lehrer's language of cellular algebras. The aim is to begin to connect the new results from topology to well-established representation theoretic understandings of these objects.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Logic