On a family of quivers related to the Gibbons-Hermsen system
| Autor: | Alberto Tacchella |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Ring (mathematics)
Group (mathematics) FOS: Physical sciences General Physics and Astronomy Natural number Mathematical Physics (math-ph) Path algebra Algebra Combinatorics Mathematics - Symplectic Geometry 14A22 (Primary) 37J35 16G20 (Secondary) FOS: Mathematics Symplectic Geometry (math.SG) Rank (graph theory) Geometry and Topology Mathematical Physics Symplectic geometry Mathematics |
| Popis: | We introduce a family of quivers $Z_{r}$ (labeled by a natural number $r\geq 1$) and study the non-commutative symplectic geometry of the corresponding doubles $\mathbf{Q}_{r}$. We show that the group of non-commutative symplectomorphisms of the path algebra $\mathbb{C}\mathbf{Q}_{r}$ contains two copies of the group $\mathrm{GL}_{r}$ over a ring of polynomials in one indeterminate, and that a particular subgroup $\mathcal{P}_{r}$ (which contains both of these copies) acts on the completion $\mathcal{C}_{n,r}$ of the phase space of the $n$-particles, rank $r$ Gibbons-Hermsen integrable system and connects each pair of points belonging to a certain dense open subset of $\mathcal{C}_{n,r}$. This generalizes some known results for the cases $r=1$ and $r=2$. 29 pages. v3: keeps some introductory material left out of the journal version |
| Databáze: | OpenAIRE |
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