Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras

2019/05/07 by Chekhov, Leonid, Mazzocco, Marta, Rubtsov, Volodya · 1 citation
#14A22 #16T99 #17B63 #32G15 #32G34 #33D80 #53D37 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1905.02772

Abstract

In this paper we study quantum del Pezzo surfaces belonging to a certain class. In particular we introduce the generalised Sklyanin-Painlevé algebra and characterise its PBW/PHS/Koszul properties. This algebra contains as limiting cases the generalised Sklyanin algebra, Etingof-Ginzburg and Etingof-Oblomkov-Rains quantum del Pezzo and the quantum monodromy manifolds of the Painlevé equations.

Cited by

• Quantisation ideals, canonical parametrisations of the unipotent group and consistent integrable systems

Related

• The Quantum Mirror to the Quartic del Pezzo Surface
• Calabi-Yau algebras
• Confluence on the Painlevé Monodromy Manifolds, their Poisson Structure and Quantisation
• Confluences of the Painleve equations, Cherednik algebras and q-Askey scheme
• Takano's Theory of Quantum Painleve Equations