Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras

Marta Mazzocco; Leonid Chekhov; Vladimir Rubtsov

doi:10.1016/j.aim.2020.107442

Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras

Marta Mazzocco, Leonid Chekhov, Vladimir Rubtsov

Mathematics

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1 Citation (Scopus)

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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.

Original language	English
Article number	107442
Journal	Advances in Mathematics
Volume	376
Early online date	17 Oct 2020
DOIs	https://doi.org/10.1016/j.aim.2020.107442
Publication status	Published - 6 Jan 2021

Bibliographical note

Funding Information:
Acknowledgements. The authors are grateful to Yu. Berest, R. Berger, F. Eshmatov, P. Etingof, D. Gurevich, N. Iyudu, T. Kelly, T. Koornwinder, M. Gross, B. Pym, V. Sokolov, P. Terwilliger, A. Zhedanov for helpful discussions. Our special thanks to Geoffrey Powell who carefully read our first version and made several useful remarks and to the referee whose remarks were truly helpful. This research was supported by the EPSRC Research Grant EP/P021913/1 , by the Hausdorff Institute , by ANR DIADEMS and MPIM (Bonn) and SISSA (Trieste). V.R. was partly supported by the project IPaDEGAN (H2020-MSCA-RISE-2017), Grant Number 778010 , and by the Russian Foundation for Basic Research under the Grants RFBR 18-01-00461 and 16-51-53034-716 GFEN.

Publisher Copyright:
© 2020 Elsevier Inc.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

Calabi-Yau algebras
Mini-versal deformations
PBW
Painlevé equations
Sklyanin algebra

ASJC Scopus subject areas

General Mathematics

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1905.02772Accepted author manuscript, 527 KBLicence: Other (please provide link to licence statement

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title = "Quantised Painlev{\'e} monodromy manifolds, Sklyanin and Calabi-Yau algebras",

abstract = "In this paper we study quantum del Pezzo surfaces belonging to a certain class. In particular we introduce the generalised Sklyanin-Painlev{\'e} 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 Painlev{\'e} equations.",

keywords = "Calabi-Yau algebras, Mini-versal deformations, PBW, Painlev{\'e} equations, Sklyanin algebra",

author = "Marta Mazzocco and Leonid Chekhov and Vladimir Rubtsov",

note = "Funding Information: Acknowledgements. The authors are grateful to Yu. Berest, R. Berger, F. Eshmatov, P. Etingof, D. Gurevich, N. Iyudu, T. Kelly, T. Koornwinder, M. Gross, B. Pym, V. Sokolov, P. Terwilliger, A. Zhedanov for helpful discussions. Our special thanks to Geoffrey Powell who carefully read our first version and made several useful remarks and to the referee whose remarks were truly helpful. This research was supported by the EPSRC Research Grant EP/P021913/1 , by the Hausdorff Institute , by ANR DIADEMS and MPIM (Bonn) and SISSA (Trieste). V.R. was partly supported by the project IPaDEGAN (H2020-MSCA-RISE-2017), Grant Number 778010 , and by the Russian Foundation for Basic Research under the Grants RFBR 18-01-00461 and 16-51-53034-716 GFEN. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2021",

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AU - Mazzocco, Marta

AU - Chekhov, Leonid

AU - Rubtsov, Vladimir

N1 - Funding Information: Acknowledgements. The authors are grateful to Yu. Berest, R. Berger, F. Eshmatov, P. Etingof, D. Gurevich, N. Iyudu, T. Kelly, T. Koornwinder, M. Gross, B. Pym, V. Sokolov, P. Terwilliger, A. Zhedanov for helpful discussions. Our special thanks to Geoffrey Powell who carefully read our first version and made several useful remarks and to the referee whose remarks were truly helpful. This research was supported by the EPSRC Research Grant EP/P021913/1 , by the Hausdorff Institute , by ANR DIADEMS and MPIM (Bonn) and SISSA (Trieste). V.R. was partly supported by the project IPaDEGAN (H2020-MSCA-RISE-2017), Grant Number 778010 , and by the Russian Foundation for Basic Research under the Grants RFBR 18-01-00461 and 16-51-53034-716 GFEN. Publisher Copyright: © 2020 Elsevier Inc. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2021/1/6

Y1 - 2021/1/6

N2 - 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.

AB - 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.

KW - Calabi-Yau algebras

KW - Mini-versal deformations

KW - PBW

KW - Painlevé equations

KW - Sklyanin algebra

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JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 107442

ER -

Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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