Cyclotomic Birman--Wenzl--Murakami algebras, II: Admissibility Relations and Freeness

2006/12/02 by Goodman, Frederick M., Mosley, Holly Hauschild
#16G99 #20C08 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0612065

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.

Related

• Cyclotomic Birman--Wenzl--Murakami algebras, I: Freeness and realization as tangle algebras
• On the freeness of the cyclotomic BMW algebras: admissibility and an isomorphism with the cyclotomic Kauffman tangle algebras
• Comparison of Admissibility Conditions for Cyclotomic Birman--Wenzl--Murakami Algebras
• The Cyclotomic Birman-Murakami-Wenzl Algebras
• Affine Birman-Wenzl-Murakami Algebras and Tangles in the Solid Torus