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- W1661537668 abstract "Inspired by the swapping algebra and the rank $n$ cross-ratio introduced by F. Labourie, to characterize moduli spaces of of rank $n$ and their natural Poisson structures, we introduce a quotient ring $mathcal{Z}_n(mathcal{P})$ equipped with the swapping Poisson bracket---the rank $n$ swapping algebra to characterize the moduli spaces of cross ratios in rank $n$. We prove that $mathcal{Z}_n(mathcal{P})$ inherits a Poisson structure from the swapping bracket. To consider the cross-ratios in the fraction ring of $mathcal{Z}_n(mathcal{P})$, by interpreting $mathcal{Z}_n(mathcal{P})$ by a geometric model, we prove that $mathcal{Z}_n(mathcal{P})$ is an integral domain. This is first step of our program. We will relate the rank $n$ swapping algebra to Fock-Goncharov coordinates and discrete integrable systems in our upcomming papers." @default.
- W1661537668 created "2016-06-24" @default.
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- W1661537668 date "2014-11-11" @default.
- W1661537668 modified "2023-09-27" @default.
- W1661537668 title "Rank n swapping algebra" @default.
- W1661537668 hasPublicationYear "2014" @default.
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