We describe a unifying framework for the systematic construction of integrable deformations
of integrable σ-models within the Hamiltonian formalism. It applies equally to both the'Yang …

We present an analysis of the canonical structure of the Wess-Zumino-Witten theory with
untwisted conformal boundary conditions. The phase space of the boundary theory on a …

We construct a Poisson isomorphism between the formal Poisson manifolds g* and G*,
where g is a finite-dimensional quasitriangular Lie bialgebra. Here g* is equipped with its …

Poisson-Lie (PL) dynamical r-matrices are generalizations of dynamical r-matrices, where
the base is a Poisson-Lie group. We prove analogues of basic results for these r-matrices …

Abstract According to Etingof and Varchenko, the classical dynamical Yang-Baxter equation
is a guarantee for the consistency of the Poisson bracket on certain Poisson-Lie groupoids …

The zero modes of the chiral SU (n) WZNW model give rise to an intertwining quantum
matrix algebra Script A generated by an n× n matrix a=(ai α), i, α= 1,..., n (with noncommuting …

The symplectic and Poisson structures of the Liouville theory are derived from the SL (2, R)
WZNW theory by gauge invariant Hamiltonian reduction. Causal non-equal time Poisson …

We describe a relationship of the classical dynamical Yang-Baxter equation with the
following elementary problem for Clifford algebras: Given a vector space $ V $ with …

We review the concept of the (anomalous) Poisson–Lie symmetry in a way that emphasizes
the notion of Poisson–Lie Hamiltonian. The language that we develop turns out to be very …

A dynamical r-matrix is associated with every self-dual Lie algebra A which is graded by
finite-dimensional subspaces as A=⊕ n∈ ZA n, where A n is dual to A− n with respect to the …