Moduli spaces of sheaves on Hirzebruch surfaces, Poisson geometry, and integrable ...
Simple finite-dimensional noncommutative Jordan superalgebras
Lie and Jordan algebras, their representations and generalizations
| Full text | |
| Author(s): |
Chuno, Eber
Total Authors: 1
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| Document type: | Journal article |
| Source: | Colloquium Mathematicum; v. 161, n. 1, p. 22-pg., 2020-01-01. |
| Abstract | |
We present a non-local Poisson bracket defined on the phase space G(u,v)/H, where G(u,v) is a Coxeter double Bruhat cell of GL(n) and H is the subgroup of diagonal matrices. The non-local Poisson bracket is written in an appropriate set of coordinates of G(u,v)/H derived from a set of factorization parameters for G(u,v). We show that the non-local Poisson bracket corresponds to the Atiyah-Hitchin bracket under the Moser map. As a consequence, the non-local Poisson bracket is compatible with a quadratic Poisson bracket obtained by M. Gekhtman, M. Shapiro and A. Vainshtein (2011). (AU) | |
| FAPESP's process: | 14/08512-3 - Cluster algebras and integrable systems |
| Grantee: | Eber Daniel Chuno Vizarreta |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |