Hall categories and KLR categorification
Abstract
This paper is the first step in the project of categorifying the bialgebra structure on the half of quantum group $U_{q}(\mathfrak{g})$ by using geometry and Hall algebras. We equip the category of Dmodules on the moduli stack of objects of the category $Rep_{\mathbb{C}}(Q)$ of representations of a quiver with the structure of an algebra object in the category of stable $\infty$categories. The data for this construction is provided by an extension of the Waldhausen construction for the category $Rep_{\mathbb{C}}(Q)$. We discuss the connection to the KhovanovLaudaRouquier categorification of half of the quantum group $U_{q}(\mathfrak{g})$ associated to the quiver $Q$ and outline our approach to the categorification of the bialgebra structure.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 arXiv:
 arXiv:1810.06960
 Bibcode:
 2018arXiv181006960G
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Category Theory;
 Mathematics  Quantum Algebra