Quantum dynamical Yang-Baxter equation over a nonabelian base

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In this paper we consider dynamical r-matrices over a nonabelian base. There are two main results. First, corresponding to a fat reductive decomposition of a Lie algebra g = h ⊕ m, we construct geometrically a non-degenerate triangular dynamical r-matrix using symplectic fibrations. Second, we prove that a triangular dynamical r-matrix r : h* → Λ2g naturally corresponds to a Poisson manifold h* × G. A special type of quantization of this Poisson manifold, called compatible star products in this paper, yields a generalized version of the quantum dynamical Yang-Baxter equation (or Gervais-Neveu-Felder equation). As a result, the quantization problem of a general dynamical r-matrix is proposed.

Original languageEnglish (US)
Pages (from-to)475-495
Number of pages21
JournalCommunications In Mathematical Physics
Volume226
Issue number3
DOIs
StatePublished - Apr 1 2002

Fingerprint

Yang-Baxter Equation
R-matrix
Poisson Manifolds
matrices
Triangular
Quantization
Star Products
fats
Fibration
Lie Algebra
algebra
decomposition
Decompose
stars
products

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Quantum dynamical Yang-Baxter equation over a nonabelian base. / Xu, Ping.

In: Communications In Mathematical Physics, Vol. 226, No. 3, 01.04.2002, p. 475-495.

Research output: Contribution to journalArticle

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