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  Derived traces of Soergel categories

Gorsky, E., Hogancamp, M., & Wedrich, P. (2022). Derived traces of Soergel categories. International Mathematics Research Notices, 2022(15), 11304-11400. doi:10.1093/imrn/rnab019.

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2002.06110.pdf (Preprint), 904KB
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 Creators:
Gorsky, Eugene, Author
Hogancamp, Matthew, Author
Wedrich, Paul1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Geometric Topology, Algebraic Geometry, Quantum Algebra, Representation Theory
 Abstract: We study two kinds of categorical traces of (monoidal) dg categories, with
particular interest in categories of Soergel bimodules. First, we explicitly
compute the usual Hochschild homology, or derived vertical trace, of the
category of Soergel bimodules in arbitrary types. Secondly, we introduce the
notion of derived horizontal trace of a monoidal dg category and compute the
derived horizontal trace of Soergel bimodules in type A. As an application we
obtain a derived annular Khovanov-Rozansky link invariant with an action of
full twist insertion, and thus a categorification of the HOMFLY-PT skein module
of the solid torus.

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Language(s): eng - English
 Dates: 2022
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2002.06110
DOI: 10.1093/imrn/rnab019
 Degree: -

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Title: International Mathematics Research Notices
  Abbreviation : IMRN
Source Genre: Journal
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Publ. Info: Oxford University Press
Pages: - Volume / Issue: 2022 (15) Sequence Number: - Start / End Page: 11304 - 11400 Identifier: -