Coxeter's frieze patterns and discretization of the Virasoro orbit

Valentin Ovsienko; Serge Tabachnikov

doi:10.1016/j.geomphys.2014.07.002

Coxeter's frieze patterns and discretization of the Virasoro orbit

Valentin Ovsienko, Serge Tabachnikov

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We show that the space of classical Coxeter's frieze patterns can be viewed as a discrete version of a coadjoint orbit of the Virasoro algebra. The canonical (cluster) (pre)symplectic form on the space of frieze patterns is a discretization of Kirillov's symplectic form. We relate a continuous version of frieze patterns to conformal metrics of constant curvature in dimension 2.

Original language	English (US)
Pages (from-to)	373-381
Number of pages	9
Journal	Journal of Geometry and Physics
Volume	87
DOIs	https://doi.org/10.1016/j.geomphys.2014.07.002
State	Published - Jan 1 2015

All Science Journal Classification (ASJC) codes

Mathematical Physics
Physics and Astronomy(all)
Geometry and Topology

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10.1016/j.geomphys.2014.07.002

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title = "Coxeter's frieze patterns and discretization of the Virasoro orbit",

abstract = "We show that the space of classical Coxeter's frieze patterns can be viewed as a discrete version of a coadjoint orbit of the Virasoro algebra. The canonical (cluster) (pre)symplectic form on the space of frieze patterns is a discretization of Kirillov's symplectic form. We relate a continuous version of frieze patterns to conformal metrics of constant curvature in dimension 2.",

author = "Valentin Ovsienko and Serge Tabachnikov",

note = "Funding Information: We are grateful to Boris Khesin and Sophie Morier-Genoud for enlightening discussions. V. O. was partially supported by the PICS05974 “PENTAFRIZ” of CNRS . S.T. was partially supported by the NSF grant DMS-1105442 . Publisher Copyright: {\textcopyright} 2014 Elsevier B.V.",

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doi = "10.1016/j.geomphys.2014.07.002",

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AU - Ovsienko, Valentin

AU - Tabachnikov, Serge

N1 - Funding Information: We are grateful to Boris Khesin and Sophie Morier-Genoud for enlightening discussions. V. O. was partially supported by the PICS05974 “PENTAFRIZ” of CNRS . S.T. was partially supported by the NSF grant DMS-1105442 . Publisher Copyright: © 2014 Elsevier B.V.

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Y1 - 2015/1/1

N2 - We show that the space of classical Coxeter's frieze patterns can be viewed as a discrete version of a coadjoint orbit of the Virasoro algebra. The canonical (cluster) (pre)symplectic form on the space of frieze patterns is a discretization of Kirillov's symplectic form. We relate a continuous version of frieze patterns to conformal metrics of constant curvature in dimension 2.

AB - We show that the space of classical Coxeter's frieze patterns can be viewed as a discrete version of a coadjoint orbit of the Virasoro algebra. The canonical (cluster) (pre)symplectic form on the space of frieze patterns is a discretization of Kirillov's symplectic form. We relate a continuous version of frieze patterns to conformal metrics of constant curvature in dimension 2.

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DO - 10.1016/j.geomphys.2014.07.002

M3 - Article

AN - SCOPUS:84912019497

SN - 0393-0440

VL - 87

SP - 373

EP - 381

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

Coxeter's frieze patterns and discretization of the Virasoro orbit

Abstract

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