The Jucys-Murphy basis and semisimplicty criteria for the $q$-Brauer algebra
Hebing Rui, Mei Si, Linliang Song
TL;DR
This paper constructs Jucys-Murphy elements and bases for the $q$-Brauer algebra, providing criteria for its semisimplicity over any field, advancing understanding of its algebraic structure.
Contribution
It introduces the Jucys-Murphy basis for the $q$-Brauer algebra and establishes a complete semisimplicity criterion applicable over arbitrary fields.
Findings
Constructed Jucys-Murphy elements for the $q$-Brauer algebra.
Provided necessary and sufficient conditions for semisimplicity.
Extended semisimplicity criteria to arbitrary fields.
Abstract
We construct the Jucys-Murphy elements and the Jucys-Murphy basis for the -Brauer algebra in the sense of Mathas[11]. We also give a necessary and sufficient condition for the -Brauer algebra being (split) semisimple over an arbitrary field.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons