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The Birman-Murakami-Wenzl algebras of type E_n

Cohen, Arjeh M. and Wales, David B. (2011) The Birman-Murakami-Wenzl algebras of type E_n. Transformation Groups, 16 (3). pp. 681-715. ISSN 1083-4362. https://resolver.caltech.edu/CaltechAUTHORS:20110914-114035979

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Abstract

The Birman-Murakami-Wenzl algebras (BMW algebras) of type E_ n for n = 6, 7, 8 are shown to be semisimple and free over the integral domain Z[δ^(±1),l^(±1),m]/(m1−δ)(l−l^(−1)) of ranks 1,440,585; 139,613,625; and 53,328, 069,225. We also show they are cellular over suitable rings. The Brauer algebra of type E_n is a homomorphic ring image and is also semisimple and free of the same rank as an algebra over the ring Z[δ^(±1)]. A rewrite system for the Brauer algebra is used in bounding the rank of the BMW algebra above. The generalized Temperley-Lieb algebra of type E_n turns out to be a subalgebra of the BMW algebra of the same type. So, the BMW algebras of type E_n share many structural properties with the classical ones (of type A_n) and those of type D_n .


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00031-011-9150-9DOIArticle
https://rdcu.be/bPBJDPublisherFree ReadCube access
https://arxiv.org/abs/1101.3544arXivDiscussion Paper
Additional Information:© 2011 Birkhäuser Boston. Dedicated to professor T. A. Springer on the occasion of his 85th birthday. Received January 7, 2011. Accepted April 28, 2011. Published online June 17, 2011.
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:3
Classification Code:AMS classification: 16K20; 17Bxx; 20F05; 20F36; 20M05
Record Number:CaltechAUTHORS:20110914-114035979
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110914-114035979
Official Citation:Cohen, A.M. & Wales, D.B. Transformation Groups (2011) 16: 681. https://doi.org/10.1007/s00031-011-9150-9
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:25345
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:16 Sep 2011 16:45
Last Modified:03 Oct 2019 03:05

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