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THE HALL ALGEBRAS OF SURFACES I

Part of: Symplectic geometry, contact geometry Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  22 October 2018

Benjamin Cooper  and
Peter Samuelson
Benjamin Cooper
Affiliation:
University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, IA 52242-1419, USA ([email protected])
Peter Samuelson
Affiliation:
University of California, Riverside, Department of Mathematics, 900 University Ave., Riverside 92521, USA ([email protected])
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Abstract

We study the derived Hall algebra of the partially wrapped Fukaya category of a surface. We give an explicit description of the Hall algebra for the disk with $m$ marked intervals and we give a conjectural description of the Hall algebras of all surfaces with enough marked intervals. Then we use a functoriality result to show that a graded version of the HOMFLY-PT skein relation holds among certain arcs in the Hall algebras of general surfaces.

Keywords

Fukaya categoriesHall algebrastopological field theory

MSC classification

Primary: 53D37: Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category 17B37: Quantum groups (quantized enveloping algebras) and related deformations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 3 , May 2020 , pp. 971 - 1028
Copyright
© Cambridge University Press 2018

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