The Birman-Murakami-Algebras Algebras of Type Dn
Abstract
The Birman-Murakami-Wenzl algebra (BMW algebra) of type Dn is shown to be semisimple and free of rank (2^n+1)n!!-(2^(n-1)+1)n! over a specified commutative ring R, where n!! is the product of the first n odd integers. We also show it is a cellular algebra over suitable ring extensions of R. The Brauer algebra of type Dn is the image af an R-equivariant homomorphism and is also semisimple and free of the same rank, but over the polynomial ring Z with delta and its inverse adjoined. A rewrite system for the Brauer algebra is used in bounding the rank of the BMW algebra above. As a consequence of our results, the generalized Temperley-Lieb algebra of type Dn is a subalgebra of the BMW algebra of the same type.
Keywords
Cite
@article{arxiv.0704.2743,
title = {The Birman-Murakami-Algebras Algebras of Type Dn},
author = {Arjeh M. Cohen and D. A. H. Gijsbers and David B. Wales},
journal= {arXiv preprint arXiv:0704.2743},
year = {2011}
}
Comments
32 pages. This is a greatly expanded version of the earlier arXiv version which was titled "The BMW Algebras of Type Dn"