Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0704.2743

The Birman-Murakami-Algebras Algebras of Type Dn

Arjeh M. Cohen·D. A. H. Gijsbers·David B. Wales
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Birman-Murakami-Wenzl algebra (BMW algebra) of type Dn 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!! is the product of the first n odd integers. We also show it is a cellular algebra over suitable ring extensions of R. The Brauer algebra of type Dn is the image af an R-equivariant homomorphism and is also semisimple and free of the same rank, but over the polynomial ring Z with delta and its inverse adjoined. 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 Dn is a subalgebra of the BMW algebra of the same type.

Explore related subjects

math.RTmath.GR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Arjeh M. Cohen, D. A. H. Gijsbers, David B. Wales. 2011-05-02. The Birman-Murakami-Algebras Algebras of Type Dn. https://arxiv.org/abs/0704.2743

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Hook fusion procedure for hyper-octahedral groups

We derive a new expression for the diagonal matrix elements of irreducible representations of the hyperoctahedral group. This expression is obtained using Grime's hook fusion procedure for symmetric groups, which minimizes the number of auxiliary parameters required in the fusion process.

math.RT↗
arXiv2026

Reductive monoids over general base

We develop a theory of affine algebraic monoids over connected base schemes whose unit groups are split reductive groups. Our main result is a classification theorem for such objects, generalizing works of Vinberg and Rittatore over a field. As applications, we obtain combinatorial descriptions and normality properties of orbit closures, prove a Steinberg-type theorem on adjoint quotients of split reductive monoids, and construct finite type integral models of the Vinberg monoids.

math.RT↗
arXiv2026

Finitistic dimension via modules over the singularity category

We combine results of Rickard and Shaul with methods of intrinsic homological algebra and the theory of purity to prove that the finiteness of the big finitistic dimension of an Artin algebra is an intrinsic property of the singularity category of its opposite algebra, via its category of modules. This `object-free' approach complements work of Dey--Šťovíček and arrives at the same conclusion: the finiteness of the finitistic dimension of Artin algebras is a singular invariant (of the opposite algebras). In fact, our characterisation can be used to prove that finite finitistic dimension descends along certain fully faithful functors between singularity categories. We include an appendix where we explain how our methods can be used to prove non-existence of bounded t-structures on singularity categories.

math.RT↗