Semistable Chow–Hall algebras of quivers and quantized Donaldson–Thomas invariants

Franzen, Hans; Reineke, Markus

doi:10.2140/ant.2018.12.1001

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Semistable Chow–Hall algebras of quivers and quantized Donaldson–Thomas invariants

Hans Franzen and Markus Reineke

Vol. 12 (2018), No. 5, 1001–1025

DOI: 10.2140/ant.2018.12.1001

Abstract

The semistable ChowHa of a quiver with stability is defined as an analog of the cohomological Hall algebra of Kontsevich and Soibelman via convolution in equivariant Chow groups of semistable loci in representation varieties of quivers. We prove several structural results on the semistable ChowHa, namely isomorphism of the cycle map, a tensor product decomposition, and a tautological presentation. For symmetric quivers, this leads to an identification of their quantized Donaldson–Thomas invariants with the Chow–Betti numbers of moduli spaces.

Keywords

cohomological Hall algebra, Donaldson–Thomas invariants, quiver moduli

Mathematical Subject Classification 2010

Primary: 14N35

Secondary: 14C15, 16G20

Milestones

Received: 25 April 2016

Revised: 13 February 2018

Accepted: 31 March 2018

Published: 31 July 2018

Authors

Hans Franzen
Mathematisches Institut Universität Bonn Germany

Markus Reineke
Faculty of Mathematics Ruhr-Universität Bochum Germany

Vol. 12, No. 5, 2018