2007/04/20 by Arjeh M. Cohen, Cohen, Arjeh M., D. A. H. Gijsbers +3
Mathematics · #16K20 #17Bxx #20F05 #20F36 #20M05 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:16K20 #msc:17Bxx #msc:20F05 #msc:20F36 #msc:20M05
paper · pdf · doi:10.48550/arxiv.0704.2743
32 pages. This is a greatly expanded version of the earlier arXiv version which was titled "The BMW Algebras of Type Dn"
arxiv created 2011/05/02 · arxiv updated 2011/05/03
The Birman-Murakami-Wenzl algebra (BMW algebra) of type Dn is shown to be semisimple and free of rank (2n+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.