A Remark on BMW Algebra, q-Schur Algebras and Categorification

2012/03/31 by Pedro Vaz, Emmanuel Wagner
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Categorification #Cellular algebra #Filtered algebra #Geometric and Algebraic Topology #Mathematics #Polynomial #Pure mathematics #math.QA

paper · pdf · doi:10.4153/cjm-2013-018-1

published as Can. J. Math.-J. Can. Math. 66 (2014) 453-480 · 26 pages. v2: minor changes

openalex publication_date 2013/05/06 · arxiv created 2013/05/10 · openalex created_date 2019/06/27 · arxiv updated 2019/08/15 · openalex updated_date 2026/08/05

Abstract

Abstract We prove that the two-variable BMW algebra embeds into an algebra constructed from the HOMFLY-PT polynomial. We also prove that the so2N -BMW algebra embeds in the q -Schur algebra of type A. We use these results to suggest a schema providing categorifications of the 2N-BMW algebra.

Citations

• Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
• Matrix factorizations and link homology II
• An invariant of regular isotopy
• A basis for the Birman-Wenzl algebra
• On the Kauffman-Vogel and the Murakami-Ohtsuki-Yamada Graph Polynomials