Reference : Rank n swapping algebra for PGLn Fock--Goncharov X moduli space
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/39495
Rank n swapping algebra for PGLn Fock--Goncharov X moduli space
English
Sun, Zhe mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
2000
Mathematische Annalen
Springer
Yes (verified by ORBilu)
International
0025-5831
1432-1807
Heidelberg
Germany
[en] Poisson algebra homomorphism ; rank n swapping algebra ; Fock–Goncharov X moduli space
[en] The rank $n$ swapping multifraction algebra is a field of cross ratios up to $(n+1)\times (n+1)$-determinant relations equipped with a Poisson bracket, called the {\em swapping bracket}, defined on the set of ordered pairs of points of a circle using linking numbers. Let $D_k$ be a disk with $k$ points on its boundary. The moduli space $\mathcal{X}_{\operatorname{PGL}_n,D_k}$ is the building block of the Fock--Goncharov $\mathcal{X}$ moduli space for any general surface. Given any ideal triangulation of $D_k$, we find an injective Poisson algebra homomorphism from the rank $n$ Fock--Goncharov algebra for $\mathcal{X}_{\operatorname{PGL}_n,D_k}$ to the rank $n$ swapping multifraction algebra with respect to the Atiyah--Bott--Goldman Poisson bracket and the swapping bracket. Two such injective Poisson algebra homomorphisms related to two ideal triangulations $\mathcal{T}$ and $\mathcal{T}'$ are compatible with each other under the flips.
http://hdl.handle.net/10993/39495
10.1007/s00208-020-02025-1
https://arxiv.org/abs/1503.00918
FP7 ; 246918 - HIGHTEICH - Higher Teichmüller-Thurston Theory: Representations of Surface Groups in PSL(n,R).
FnR ; FNR13242285 > Zhe Sun > > COmbinatorial and ALgebraic Aspects of Surface group representations. > 01/09/2018 > 31/08/2020 > 2017

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
SWAPFG.pdfarXiv versionPublisher postprint819.58 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.