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FAITHFULNESS OF THE 2-BRAID GROUP VIA ZIGZAG ALGEBRA IN TYPE B

Part of: Special aspects of infinite or finite groups Connections with homological algebra and category theory

Published online by Cambridge University Press:  27 October 2023

EDMUND HENG Open the ORCID record for EDMUND HENG [Opens in a new window]  and
KIE SENG NGE Open the ORCID record for KIE SENG NGE [Opens in a new window]
EDMUND HENG*
Affiliation:
Institut des Hautes Études Scientifiques, 35, Route de Chartres, 91440 Bures-sur-Yvette, France
KIE SENG NGE
Affiliation:
School of Mathematics and Physics, Department of Mathematics and Applied Mathematics, Xiamen University Malaysia, Block A4, Jalan Sunsuria, Bandar Sunsuria, 43900 Sepang, Selangor Darul Ehsan, Malaysia e-mail: kieseng.nge@xmu.edu.my
*
e-mail: heng@ihes.fr
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Abstract

We show that a certain category of bimodules over a finite-dimensional quiver algebra known as a type B zigzag algebra is a quotient category of the category of type B Soergel bimodules. This leads to an alternate proof of Rouquier’s conjecture on the faithfulness of the 2-braid groups for type B.

Keywords

2-braid groupsSoergel bimodulesTemperley–Lieb algebrastype B braid groups

MSC classification

Primary: 20F36: Braid groups; Artin groups
Secondary: 20J05: Homological methods in group theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 117 , Issue 1 , August 2024 , pp. 67 - 84
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Oded Yacobi

References

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