TL;DR
This paper introduces a new q-deformation of Brauer's algebra, expanding the algebraic framework with potential applications in subfactor theory and fusion categories related to symmetric spaces.
Contribution
It defines a novel q-deformation of Brauer's algebra that includes Hecke algebras of type A and analyzes its structure and quotients.
Findings
Defined a new q-Brauer algebra containing Hecke algebras of type A
Determined the generic and semisimple quotient structures
Suggested applications in subfactor theory and fusion categories
Abstract
We define a new -deformation of Brauer's centralizer algebra which contains Hecke algebras of type as unital subalgebras. We determine its generic structure as well as the structure of certain semisimple quotients. This is expected to have applications for constructions of subfactors of type II factors and for module categories of fusion categories of type corresponding to certain symmetric spaces.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry