Non-commutative integrability of the Grassmann pentagram map

DOI10.1016/j.aim.2020.107309OpenAlexW3045801356MaRDI QIDQ2196620

Nicholas Ovenhouse

Publication date: 3 September 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.11742

zbMATH Keywords

integrable systemsPoisson geometrypentagram maps

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Applications of Lie algebras and superalgebras to integrable systems (17B80) Poisson algebras (17B63) Cluster algebras (13F60) Integrable difference and lattice equations; integrability tests (39A36) Completely integrable discrete dynamical systems (37J70)

Related Items (2)

Pentagram maps and refactorization in Poisson-Lie groups ⋮ Pentagram-type maps and the discrete KP equation

Cites Work

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• Integrable cluster dynamics of directed networks and pentagram maps
• Poisson geometry of directed networks in an annulus
• The pentagram map and \(Y\)-patterns
• Poisson structures on moduli spaces of representations
• The symplectic nature of fundamental groups of surfaces
• Invariant functions on Lie groups and Hamiltonian flows of surface group representations
• The invariant theory of \(n\times n\) matrices
• Quasideterminants
• Poisson geometry of directed networks in a disk
• The pentagram map on Grassmannians
• Moduli spaces of local systems and higher Teichmüller theory
• Cluster algebras I: Foundations
• Quasi-Poisson Structures on Representation Spaces of Surfaces
• Cluster algebras IV: Coefficients
• Double Poisson algebras
• Dimers and cluster integrable systems
• The pentagram map: a discrete integrable system

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