2011/01/18 by Arjeh M. Cohen, Cohen, Arjeh M., David B. Wales +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.1101.3544
33 pages
arxiv created 2011/01/18 · openalex publication_date 2011/01/18 · arxiv updated 2011/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Birman-Murakami-Wenzl algebras (BMW algebras) of type En for n=6,7,8 are shown to be semisimple and free over a quotient of a polynomial algebra 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 En is a homomorphic ring image and is also semisimple and free of the same rank as an algebra over a different polynomial ring. 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 En share many structural properties with the classical ones (of type An) and those of type Dn.