The Birman-Murakami-Wenzl algebras of type Dn

A.M. Cohen, D.A.H. Gijsbers, D.B. Wales

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

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 R-equivariant homomorphism and is also semisimple and free of the same rank, but over the ring Z [d±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.
Original languageEnglish
Pages (from-to)22-55
JournalCommunications in Algebra
Volume42
Issue number1
DOIs
Publication statusPublished - 2014

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