The Hecke bicategory
type: Item
instance of: scholarly article
title: The Hecke bicategory
zbMATH Open document ID: 1305.18006
author: Alexander E. Hoffnung
published in: Axioms
publication date: 2014-08-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1007.1931
review text: Summary: We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid -- the category of permutation representations of a finite group. As an immediate consequence, we obtain a categorification of the Hecke algebra. We suggest an explicit connection to new higher isomorphisms arising from incidence geometries, which are solutions of the Zamolodchikov tetrahedron equation. This paper is expository in style and is meant as a companion to [\textit{J. C. Baez} et al., Theory Appl. Categ. 24, 489--553 (2010; Zbl 1229.18003)] and an exploration of structures arising in the work in progress [\textit{J. C. Baez} and the author, ``Higher dimensional algebra. VIII: The Hecke bicategory'', \url{http://math.ucr.edu/home/baez/hecke.pdf}], which introduces the Hecke bicategory in detail.
Mathematics Subject Classification ID: 18B40
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 6330799
zbMATH Keywords: Hecke algebras
zbMATH Keywords: categorification
zbMATH Keywords: groupoidification
zbMATH Keywords: Yang-Baxter equations
zbMATH Keywords: Zamalodchikov tetrahedron equations
zbMATH Keywords: spans
zbMATH Keywords: enriched bicategories
zbMATH Keywords: buildings
zbMATH Keywords: incidence geometries
MaRDI profile type: Publication
OpenAlex ID: W2020047848
arXiv ID: 1007.1931
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DOI: 10.3390/AXIOMS1030291
description: scientific article