O(d,d) transformations preserve classical integrability

Transformations that Preserve Learnability

On certain semigroups of transformations that preserve double direction equivalence

Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E}It is known that TE(X) is a subsemigroup of TX. In this paper, we discussthe Green's *-relations, certain *-ideal and certain Rees quotient semigroup for TE(X).

Lectures on Classical Integrability

We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of

Classical Open String Integrability

We present a simple procedure to construct non-local conserved charges for classical open strings on coset spaces. This is done by including suitable reflection matrices on the classical transfer matrix. The reflection matrices must obey certain conditions for the charges to be conserved and in involution. We then study bosonic open strings on AdS5×S. We consider boundary conditions correspondi...

Classical and Quantum Integrability

It is a well-known problem to decide if a classical hamiltonian system that is integrable, in the Liouville sense, can be quantised to a quantum integrable system. We identify the obstructions to do so, and show that the obstructions vanish under certain conditions. 2000 Math. Subj. Class. 81S10.