Vol. 12, No. 5, 2018

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Semistable Chow–Hall algebras of quivers and quantized Donaldson–Thomas invariants

Hans Franzen and Markus Reineke

Vol. 12 (2018), No. 5, 1001–1025
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