These are pedagogical lecture notes discussing current–current deformations of 2-
dimensional field theories. The deformations that are considered here are generated …

We give an AdS/CFT interpretation to homogeneous Yang–Baxter deformations of the AdS
5× S 5 superstring as noncommutative deformations of the dual gauge theory, going well …

Deformation quantization, which gives a development of quantum mechanics independent
of the operator algebra formulation, and quantum groups, which arose from the inverse …

Light-cone gauge-fixed sigma models on AdS n× S n backgrounds play an important role in
the integrability formulation of the AdS/CFT correspondence. The string spectrum of the …

A bstract We construct actions for four dimensional noncommutative Yang-Mills theory with
star-gauge symmetry, with non-constant noncommutativity, to all orders in the …

Two one-parameter families of twists providing κ-Minkowski* product deformed spacetime
are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski …

A large class of the recently found unimodular nonabelian homogeneous Yang–Baxter
deformations of the AdS 5× S 5 superstring can be realized as sequences of noncommuting …

We settle in this paper a question left open in our paper``Modular Hecke algebras and their
Hopf symmetry'', by showing how to extend the Rankin-Cohen brackets from modular forms …

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-
action, as well as their morphisms and connections. Bimodules naturally arise when …

We define a new class of unitary solutions to the classical Yang--Baxter equation (CYBE).
These 'boundary solutions' are those which lie in the closure of the space of unitary solutions …