International Mathematics Research Notices· 2012Q1
Quasi-Poisson Structures on Representation Spaces of Surfaces
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- Q1SCImago
- 2012year
Short summary
A canonical quasi-Poisson bracket is introduced for N-dimensional linear representations of a surface's fundamental group, extending existing Poisson brackets on GLN-invariant functions.
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Key points
- Introduced a canonical quasi-Poisson bracket for N-dimensional linear representations of π1(Σ,*) for any N≥1.
- The new bracket generalizes the known Poisson bracket on GLN-invariant functions on the representation space.
- The construction utilizes a quasi-Poisson double algebra structure on the group algebra of π1(Σ,*).
AI-generated from the title and abstract; the full text is not read.
Abstract
Given an oriented surface Σ with base point *∈∂Σ, we introduce for all N≥1, a canonical quasi-Poisson bracket on the space of N-dimensional linear representations of π1(Σ,*). Our bracket extends the well-known Poisson bracket on GLN-invariant functions on this space. Our main tool is a natural structure of a quasi-Poisson double algebra (in the sense of M. Van den Bergh) on the group algebra of π1(Σ,*).
The authors' abstract, as published at the source. International Mathematics Research Notices, 2012 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics