Remarks on Cyclotomic and Degenerate Cyclotomic BMW Algebras

TL;DR

This paper investigates the structure of cyclotomic and degenerate cyclotomic BMW algebras, establishing their cellularity and characterizing parameter sets for non-trivial quotients, thus advancing understanding of their algebraic properties.

Contribution

It demonstrates that these algebras are cellular for all parameters and characterizes the parameters allowing non-trivial cyclotomic quotients.

Findings

Algebras are cellular for arbitrary parameters.

Characterization of parameters for non-trivial quotients.

Relation between algebra structure and parameter admissibility.

Abstract

We relate the structure of cyclotomic and degenerate cyclotomic BMW algebras, for arbitrary parameter values, to that for admissible parameter values. In particular, we show that these algebras are cellular. We characterize those parameter sets for affine BMW algebras over an algebraically closed field that permit the algebras to have non--trivial cyclotomic quotients.