Monoidal categorification of genus zero skein algebras

Fuente: arXiv
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Auteurs principaux: Allegretti, Dylan G. L., Kim, Hyun Kyu, Shan, Peng
Format: Preprint
Publié: 2025
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author Allegretti, Dylan G. L.
Kim, Hyun Kyu
Shan, Peng
author_facet Allegretti, Dylan G. L.
Kim, Hyun Kyu
Shan, Peng
contents We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises as the Grothendieck ring of the bounded derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima variety of triples with monoidal structure defined by the convolution product. We thus give a monoidal categorification of the skein algebra, partially answering a question posed by D. Thurston.
format Preprint
id arxiv_https___arxiv_org_abs_2505_13332
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Monoidal categorification of genus zero skein algebras
Allegretti, Dylan G. L.
Kim, Hyun Kyu
Shan, Peng
Representation Theory
High Energy Physics - Theory
Geometric Topology
Quantum Algebra
We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises as the Grothendieck ring of the bounded derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima variety of triples with monoidal structure defined by the convolution product. We thus give a monoidal categorification of the skein algebra, partially answering a question posed by D. Thurston.
title Monoidal categorification of genus zero skein algebras
topic Representation Theory
High Energy Physics - Theory
Geometric Topology
Quantum Algebra
url https://arxiv.org/abs/2505.13332