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• W3138125725 abstract "To show that certain wild character varieties are multiplicative analogues of quiver varieties, Boalch introduced colored multiplicative quiver varieties. They form a class of (nondegenerate) Poisson varieties attached to colored quivers whose representation theory is controlled by fission algebras: noncommutative algebras generalizing the multiplicative preprojective algebras of Crawley-Boevey and Shaw. Previously, Van den Bergh exploited the Kontsevich-Rosenberg principle to prove that the natural Poisson structure of any (non-colored) multiplicative quiver variety is induced by an $H_0$-Poisson structure on the underlying multiplicative preprojective algebra. Moreover, he noticed that this noncommutative structure comes from a Hamiltonian double quasi-Poisson algebra constructed from the quiver; this offers a noncommutative analogue of quasi-Hamiltonian reduction. In this article we conjecture that, via the Kontsevich-Rosenberg principle, the natural Poisson structure on each colored multiplicative quiver variety is induced by an $H_0$-Poisson structure on the underlying fission algebra which, in turn, is obtained from a Hamiltonian double quasi-Poisson algebra attached to the colored quiver. We study some consequences of this conjecture and we prove it in two significant cases: the monochromatic interval and the monochromatic triangle." @default.
• W3138125725 created "2021-03-29" @default.
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• W3138125725 date "2021-03-18" @default.
• W3138125725 modified "2023-09-27" @default.
• W3138125725 title "On the noncommutative Poisson geometry of certain wild character varieties" @default.
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