On Cellular Algebras with Jucys Murphy Elements
Frederick M. Goodman, John Graber
TL;DR
This paper investigates the properties of Jucys-Murphy elements within cellular algebras derived from Jones basic constructions, including Brauer, BMW, and cyclotomic algebras.
Contribution
It introduces analogues of Jucys-Murphy elements in a broad class of cellular algebras and explores their structural implications.
Findings
Identification of Jucys-Murphy analogues in various cellular algebras
Analysis of their algebraic properties and representations
Extension of known results to cyclotomic cases
Abstract
We study analogues of Jucys-Murphy elements in cellular algebras arising from repeated Jones basic constructions. Examples include Brauer and BMW algebras and their cyclotomic analogues.
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