caa a22 4500 445862424 CHVBK 20180317145447.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00031-011-9150-9 doi (NATIONALLICENCE)springer-10.1007/s00031-011-9150-9 The Birman-Murakami-Wenzl algebras of type E n [Elektronische Daten] [Arjeh Cohen, David Wales] 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 $ {{{\mathbb{Z}\left[ {{\delta^{\pm 1}},{l^{\pm 1}},m} \right]}} \left/ {{\left( {m\left( {1 - \delta } \right) - \left( {l - {l^{ - 1}}} \right)} \right)}} \right.} $ 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 $ \mathbb{Z}\left[ {{\delta^{\pm 1}}} \right] $ . 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 En 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 . Springer Science+Business Media, LLC, 2011 Associative algebra nationallicence Birman-Murakami-Wenzl algebra nationallicence BMW algebra nationallicence Brauer algebra nationallicence cellular algebra nationallicence Coxeter group nationallicence generalized Temperley-Lieb algebra nationallicence root system nationallicence semisimple algebra nationallicence word problem in semigroups nationallicence Cohen Arjeh Department of Mathematics and Computer Science, Eindhoven University of Technology, POBox 513, 5600MB, Eindhoven, The Netherlands aut Wales David Mathematics Department, Sloan Lab, Caltech, 91125, Pasadena, CA, USA aut Transformation Groups SP Birkhäuser Verlag Boston 16/3(2011-09-01), 681-715 1083-4362 16:3<681 2011 16 31 https://doi.org/10.1007/s00031-011-9150-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-011-9150-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cohen Arjeh Department of Mathematics and Computer Science, Eindhoven University of Technology, POBox 513, 5600MB, Eindhoven, The Netherlands aut NATIONALLICENCE 700 1- Wales David Mathematics Department, Sloan Lab, Caltech, 91125, Pasadena, CA, USA aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/3(2011-09-01), 681-715 1083-4362 16:3<681 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer