Cohen, Arjeh M. and Gijsbers, Dié A. H. and Wales, David B. (2014) The Birman–Murakami–Wenzl Algebras of Type D_n. Communications in Algebra, 42 (1). pp. 2255. ISSN 00927872. http://resolver.caltech.edu/CaltechAUTHORS:20131118073559089

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Abstract
The Birman–Murakami–Wenzl algebra (BMW algebra) of type D_n 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!! =1·3…(2n − 1). We also show it is a cellular algebra over suitable ring extensions of R. The Brauer algebra of type D_n is the image of an Requivariant homomorphism and is also semisimple and free of the same rank, but over the ring ℤ[δ^(±1)]. 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 D_n is a subalgebra of the BMW algebra of the same type.
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Additional Information:  © 2014 Taylor & Francis Group, LLC. Received July 19, 2011. Communicated by P. Tiep. Published online: 18 Oct 2013.  
Subject Keywords:  Associative algebra; BirmanMurakamiWenzl algebra; BMW algebra: Brauer algebra; Cellular algebra; Coxeter group; Generalized TemperleyLieb algebra; Root system; Semisimple algebra; Word problem in semigroups.  
Classification Code:  2010 MSC: 16K20; 17Bxx; 20F05; 20F36; 20M05  
Record Number:  CaltechAUTHORS:20131118073559089  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20131118073559089  
Official Citation:  The Birman–Murakami–Wenzl Algebras of Type D n Arjeh M. Cohen, Dié A. H. Gijsbers, David B. Wales Communications in Algebra Vol. 42, Iss. 1, 2014  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  42511  
Collection:  CaltechAUTHORS  
Deposited By:  Ruth Sustaita  
Deposited On:  18 Nov 2013 16:23  
Last Modified:  18 Nov 2013 16:23 
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