English

Handlebody diagram algebras

Quantum Algebra 2023-08-17 v3 Geometric Topology Representation Theory

Abstract

In this paper we study handlebody versions of some classical diagram algebras, most prominently, handlebody versions of Temperley-Lieb, blob, Brauer, BMW, Hecke and Ariki-Koike algebras. Moreover, motivated by Green-Kazhdan-Lusztig's theory of cells, we reformulate the notion of (sandwich, inflated or affine) cellular algebras. We explain this reformulation and how all of the above algebras are part of this theory.

Keywords

Cite

@article{arxiv.2105.07049,
  title  = {Handlebody diagram algebras},
  author = {Daniel Tubbenhauer and Pedro Vaz},
  journal= {arXiv preprint arXiv:2105.07049},
  year   = {2023}
}

Comments

45 pages, lots of figures, revision following referees comments, to appear in Rev. Mat. Iberoam, comments welcome

R2 v1 2026-06-24T02:07:47.355Z