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The Birman–Murakami–Wenzl Algebras of Type D_n

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. 22-55. ISSN 0092-7872. doi:10.1080/00927872.2012.678955.

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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 R-equivariant 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; Birman-Murakami-Wenzl algebra; BMW algebra: Brauer algebra; Cellular algebra; Coxeter group; Generalized Temperley-Lieb algebra; Root system; Semisimple algebra; Word problem in semigroups.
Issue or Number:1
Classification Code:2010 MSC: 16K20; 17Bxx; 20F05; 20F36; 20M05
Record Number:CaltechAUTHORS:20131118-073559089
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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
Deposited By: Ruth Sustaita
Deposited On:18 Nov 2013 16:23
Last Modified:10 Nov 2021 16:24

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