Drinfeld Centers for Bicategories

Ehud Meir, Markus Szymik

Research output: Contribution to journalArticle

7 Citations (Scopus)
7 Downloads (Pure)

Abstract

We generalize Drinfeld's notion of the center of a tensor category to bicategories. In this generality, we present a spectral sequence to compute the basic invariants of Drinfeld centers: the abelian monoid of isomorphism classes of objects, and the abelian automorphism group of its identity object. There is an associated obstruction theory that explains the difference between the Drinfeld center and the center of the classifying category. For examples, we discuss bicategories of groups and bands, rings and bimodules, as well as fusion categories.
Original languageEnglish
Pages (from-to)707-735
Number of pages30
JournalDocumenta Mathematica
Volume20
Publication statusPublished - 2015

Fingerprint

Bicategory
Obstruction Theory
Tensor Category
Spectral Sequence
Bimodule
Isomorphism Classes
Monoid
Automorphism Group
Abelian group
Fusion
Ring
Generalise
Invariant
Object

Keywords

  • Drinfeld centers
  • bicategories
  • spectral sequences
  • obstruction theory
  • bands
  • bimodules
  • fusion categories

Cite this

Drinfeld Centers for Bicategories. / Meir, Ehud; Szymik, Markus.

In: Documenta Mathematica, Vol. 20, 2015, p. 707-735.

Research output: Contribution to journalArticle

Meir, E & Szymik, M 2015, 'Drinfeld Centers for Bicategories', Documenta Mathematica, vol. 20, pp. 707-735.
Meir, Ehud ; Szymik, Markus. / Drinfeld Centers for Bicategories. In: Documenta Mathematica. 2015 ; Vol. 20. pp. 707-735.
@article{86f32a66c6c44626a106ecec5b66f155,
title = "Drinfeld Centers for Bicategories",
abstract = "We generalize Drinfeld's notion of the center of a tensor category to bicategories. In this generality, we present a spectral sequence to compute the basic invariants of Drinfeld centers: the abelian monoid of isomorphism classes of objects, and the abelian automorphism group of its identity object. There is an associated obstruction theory that explains the difference between the Drinfeld center and the center of the classifying category. For examples, we discuss bicategories of groups and bands, rings and bimodules, as well as fusion categories.",
keywords = "Drinfeld centers, bicategories, spectral sequences, obstruction theory, bands, bimodules, fusion categories",
author = "Ehud Meir and Markus Szymik",
note = "Both authors were supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92).",
year = "2015",
language = "English",
volume = "20",
pages = "707--735",
journal = "Documenta Mathematica",
issn = "1431-0635",
publisher = "Deutsche Mathematiker Vereinigung",

}

TY - JOUR

T1 - Drinfeld Centers for Bicategories

AU - Meir, Ehud

AU - Szymik, Markus

N1 - Both authors were supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92).

PY - 2015

Y1 - 2015

N2 - We generalize Drinfeld's notion of the center of a tensor category to bicategories. In this generality, we present a spectral sequence to compute the basic invariants of Drinfeld centers: the abelian monoid of isomorphism classes of objects, and the abelian automorphism group of its identity object. There is an associated obstruction theory that explains the difference between the Drinfeld center and the center of the classifying category. For examples, we discuss bicategories of groups and bands, rings and bimodules, as well as fusion categories.

AB - We generalize Drinfeld's notion of the center of a tensor category to bicategories. In this generality, we present a spectral sequence to compute the basic invariants of Drinfeld centers: the abelian monoid of isomorphism classes of objects, and the abelian automorphism group of its identity object. There is an associated obstruction theory that explains the difference between the Drinfeld center and the center of the classifying category. For examples, we discuss bicategories of groups and bands, rings and bimodules, as well as fusion categories.

KW - Drinfeld centers

KW - bicategories

KW - spectral sequences

KW - obstruction theory

KW - bands

KW - bimodules

KW - fusion categories

M3 - Article

VL - 20

SP - 707

EP - 735

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

ER -