Poisson automorphisms and quiver moduli

By Markus Reineke. Journal of the Institute of Mathematics of Jussieu, 2008

109 citations recorded by the source corpus.

Abstract A factorization formula for certain automorphisms of a Poisson algebra associated with a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing formulae for Donaldson–Thomas type invariants of Kontsevich and Soibelman.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9b4304777ee612e8e9b3363361de44d2106a5e54

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Citations in the corpus

Quivers, curves, and the tropical vertex (2009, background): “h and Soibelman [10] and plays a signiﬁcant role in the program of [7]. A connection of the tropical vertex Date: September 2009. 1 2 M.GROSSANDR.PANDHARIPANDE group to (i) has been proven by Reineke [17] using wall-crossing ideas. A connection to (ii) is proven in [6]. Our aim here is to present th”
Stability structures, motivic Donaldson-Thomas invariants and cluster transformations (2008, methodology): “Recent paper [ 58 ] gives an explicit formula for d(a, b, k) in terms of the Euler characteristic of the framed moduli space of semistable representations of the quiver.”
Motivic degree zero Donaldson–Thomas invariants (2009, result): “Some formulae in the above proof appear also in recent work of Reineke [31] and Kontsevich–Soibelman [20].”
Scattering diagrams, Hall algebras and stability conditions (2016, result): “Theorem 1.3 then essentially coincides with Reineke’s result [19, Theorem 2.1] as stated in [7, Proposition 8.28].”
Canonical bases for cluster algebras (2014, methodology): “s to C − s which only crosses the walls e⊥ n,...,e ⊥ 1 in order. Note that the element of G ′attached to the wall e⊥ j acts on k\[N⊕] by zn →zn(1 + zej )−{ej,n}, which agrees with the automorphism in [R10] written as Ti j (noting that [R10] uses the opposite sign convention for the skew form {·,·}as”
A survey on maximal green sequences (2019, background): “Analogous pairs of maximal green sequences exist for all Dynkin quivers and yield generalizations of the pentagon identity due to Reineke [103], cf. [76].”
Cluster algebras and derived categories (2012, background): “Then one can show that both −C(µi(t0)) and −C(µi′(t0)) are permutation matrices and so the Kontsevich-Soibelman invariant associated with Q equals E(i) = E(i′) , which is Reineke’s identity associated with Q.”
Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants (2009, methodology): “In this section, we apply the results of the previous sections to the setup of [19].”