Casimirs of the Goldman Lie algebra of a closed surface
Pavel Etingof
Abstract
In 1986 Goldman introduced a Lie algebra structure on the linear span L of conjugacy classes of the fundamental group of a closed oriented surface. It is easy to see that the class e1 of the trivial loop is a central element in L. We prove that any central element of L is a multiple of e1 (a conjecture communicated to the author by Chas and Sullivan), and moreover that any central element of the Poisson algebra SL is a polynomial of e1.
Create a lesson
Related papers
The Haagerup VOA at c=8
Andrew Riesen
Haar measure for totally positive split real semisimple quantum groups of classical type
Kenny De Commer, Geoffrey Janssens, Wannes Malfait
Facets of nondegeneracy: central type factor groups, Heisenberg representations and Hadamard matrices
Pierre Bieliavsky, Victor Gayral, Sergey Neshveyev et al.
Triangular prism equations for near-group categories: algebraic solutions and a unitary conjecture
Huixuan He, Zhengwei Liu, Fan Lu et al.
Chiral Extensions of Cotangent Yangian
Keyou Zeng
Higher Fomin-Kirillov algebras are infinite-dimensional
N. Andruskiewitsch, I. Angiono, I. Heckenberger et al.