Article

Algebras and Representation Theory

, Volume 14, Issue 1, pp 1-39

First online:

Cyclotomic Birman–Wenzl–Murakami Algebras, II: Admissibility Relations and Freeness

  • Frederick M. GoodmanAffiliated withDepartment of Mathematics, University of Iowa Email author 
  • , Holly Hauschild MosleyAffiliated withDepartment of Mathematics, Grinnell College

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Abstract

The cyclotomic Birman-Wenzl-Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We study admissibility conditions on the ground ring for these algebras, and show that the algebras defined over an admissible integral ground ring S are free S-modules and isomorphic to cyclotomic Kauffman tangle algebras. We also determine the representation theory in the generic semisimple case, obtain a recursive formula for the weights of the Markov trace, and give a sufficient condition for semisimplicity.

Keywords

Affine and cyclotomic BMW algebras Affine and cyclotomic Hecke algebras Algebras of tangles Affine braid group

Mathematics Subject Classifications (2000)

20C08 16G99 81R50