We study properties of a scalar quantum field theory on two-dimensional non-commutative
space-times. Contrary to the common belief that non-commutativity of space-time would be a …

We develop a generalised theory of bundles and connections on them in which the role of
gauge group is played by a coalgebra and the role of principal bundle by an algebra. The …

Noncommutative algebras, rings and other noncommutative objects, along with their more
classical commutative counterparts, have become a key part of modern mathematics …

We introduce the notion of a crossed product of an al¬ gebra by a coalgebra C, which
generalises the notion of a crossed product by a bialgebra well-studied in the theory of Hopf …

All Lie bialgebra structures for the (1+ 1)-dimensional centrally extended Schrödinger
algebra are explicitly derived and proved to be of coboundary type. Therefore, since all of …

We study properties of a scalar quantum field theory on the two-dimensional
noncommutative plane with E q (2) quantum symmetry. We start from the consideration of a …

The correspondence between Poisson homogeneous spaces over a Poisson–Lie group G
and Lagrangian Lie subalgebras of the classical double $\newcommand {\gothg}{\mathfrak …

The relativistic quantum mechanics of two interacting particles is considered. We first
present a covariant formulation of kinematics and of reduced phase space, giving a short …

The Hopf algebra dual form for the non-standard uniparametric deformation of the (1+ 1)
Poincare algebra iso (1, 1) is deduced. In this framework, the quantum coordinates that …

I briefly argue for logical necessity to incorporate, besides c, ℏ, two fundamental length
scales in the symmetries associated with the interface of gravitational and quantum realms …