Dynamical r matrices and chiral WZNW phase space
نویسندگان
چکیده
منابع مشابه
ON THE CHIRAL WZNW PHASE SPACE, EXCHANGE r-MATRICES AND POISSON-LIE GROUPOIDS
This is a review of recent work on the chiral extensions of the WZNW phase space describing both the extensions based on fields with generic monodromy as well as those using Bloch waves with diagonal monodromy. The symplectic form on the extended phase space is inverted in both cases and the chiral WZNW fields are found to satisfy quadratic Poisson bracket relations characterized by monodromy d...
متن کاملDynamical r-matrices and Poisson-Lie symmetries in the chiral WZNW model
We briefly review the possible Poisson structures on the chiral WZNW phase space and discuss the associated Poisson-Lie groupoids. Many interesting dynamical r-matrices appear naturally in this framework. Particular attention is paid to the special cases in which these r-matrices satisfy the classical dynamical Yang-Baxter equation or its PoissonLie variant. Talk presented at the Workshop on In...
متن کاملThe chiral WZNW phase space as a quasi-Poisson space
It is explained that the chiral WZNW phase space is a quasi-Poisson space with respect to the ‘canonical’ Lie quasi-bialgebra which is the classical limit of Drinfeld’s quasi-Hopf deformation of the universal enveloping algebra. This exemplifies the notion of quasi-Poisson-Lie symmetry introduced recently by Alekseev and Kosmann-Schwarzbach. PACS codes: 11.25.Hf, 11.10.Kk, 11.30.Na keywords: WZ...
متن کاملThe Chiral WZNW Phase Space and its Poisson-Lie Groupoid
The precise relationship between the arbitrary monodromy dependent 2-form appearing in the chiral WZNW symplectic form and the ‘exchange r-matrix’ that governs the corresponding Poisson brackets is established. Generalizing earlier results related to diagonal monodromy, the exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter equation, wh...
متن کاملOn the Moduli Space of Classical Dynamical r-matrices
Introduction. A classical dynamical r-matrix is an l-equivariant function r : l∗ → g ⊗ g (where l, g are Lie algebras), such that r21 + r = Ω is g-invariant, which satisfies the classical dynamical Yang-Baxter equation (CDYBE). CDYBE is a differential equation, which generalizes the usual classical Yang-Baxter equation. It was introduced in 1994 by G.Felder [Fe], in the context of conformal fie...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physics of Atomic Nuclei
سال: 2002
ISSN: 1063-7788,1562-692X
DOI: 10.1134/1.1490103