Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1997

AUTHORS

Igor B. Frenkel , Vladimir G. Turaev

ABSTRACT

Various results in algebra, analysis, and geometry can be generalized by replacing the ordinary numbers (integer, real or complex) by their trigonometric analogues. For x ∈ ℂ, the trigonometric number [x]h ∈ ℂ is defined by 0.a where h ∈ ℂ\ℤ is a fixed parameter. It is clear that thus, [x]h may be viewed as a one-parameter deformation of x. The trigonometric numbers are not additive: generally speaking [x+y]h ≠ [x]h+[y]h. However, they satisfy a kind of additivity of “second order”: for any x, y, z ∈ ℂ, 0.b Many identities between ordinary numbers can be proved using only the additivity of second order and therefore allow a trigonometric deformation. More... »

PAGES

171-204

References to SciGraph publications

  • 1986-10. Fusion of the eight vertex SOS model in LETTERS IN MATHEMATICAL PHYSICS
  • 1992-05. Quantum affine algebras and holonomic difference equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1985. The Theory of Jacobi Forms in NONE
  • 1983. Tata Lectures on Theta I in NONE
  • 1995. Trigonometric Solutions of the Yang-Baxter Equation, Nets, and Hypergeometric Functions in FUNCTIONAL ANALYSIS ON THE EVE OF THE 21ST CENTURY
  • Book

    TITLE

    The Arnold-Gelfand Mathematical Seminars

    ISBN

    978-1-4612-8663-9
    978-1-4612-4122-5

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-1-4612-4122-5_9

    DOI

    http://dx.doi.org/10.1007/978-1-4612-4122-5_9

    DIMENSIONS

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