Tensor product categorifications, Verma modules and the blob 2-category

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2020-05-13 DOI:10.4171/QT/156

Abel Lacabanne, Gr'egoire Naisse, P. Vaz

引用次数: 6

Abstract

We construct a dg-enhancement of Webster's tensor product algebras that categorifies the tensor product of a universal sl2 Verma module and several integrable irreducible modules. We show that the blob algebra acts via endofunctors on derived categories of such dg-enhanced algebras in the case when the integrable modules are two-dimensional. This action intertwines with the categorical action of sl2. From the above we derive a categorification of the blob algebra.

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张量积分类，Verma模和blob 2类

我们构造了Webster张量积代数的一个g-增强，对一个泛sl2 Verma模和几个可积不可约模的张量积进行了分类。在可积模为二维的情况下，我们证明了blob代数通过内函子作用于这类dg增强代数的派生范畴。这个动作与sl2的直言动作交织在一起。由此，我们导出了blob代数的一个分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.