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Braid group actions via categorified Heisenberg complexes

Part of: Special aspects of infinite or finite groups Homological algebra Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  09 October 2013

Sabin Cautis ,
Anthony Licata  and
Joshua Sussan
Sabin Cautis*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2
Anthony Licata
Affiliation:
Mathematical Sciences Institute, Australian National University, Canberra, Australia email anthony.licata@anu.edu.au
Joshua Sussan
Affiliation:
Department of Mathematics, CUNY Medgar Evers, Brooklyn, NY, USA email jsussan@mec.cuny.edu
*
cautis@math.ubc.ca
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Abstract

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We construct categorical braid group actions from 2-representations of a Heisenberg algebra. These actions are induced by certain complexes which generalize spherical (Seidel–Thomas) twists and are reminiscent of the Rickard complexes defined by Chuang–Rouquier. Conjecturally, one can relate our complexes to Rickard complexes using categorical vertex operators.

MSC classification

Secondary: 17B65: Infinite-dimensional Lie (super)algebras 18G10: Resolutions; derived functors 20F36: Braid groups; Artin groups
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 1 , January 2014 , pp. 105 - 142
Copyright
© The Author(s) 2013 

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