We show that the crossed modules and bicovariant differential calculi on two Hopf algebras
related by a cocycle twist are in 1-1 correspondence. In particular, for quantum groups which …

Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a
deep and natural generalization of symmetry groups for certain integrable systems, and on …

The paper begins by giving an algebraic structure on a set of coset representatives for the
left action of a subgroup on a group. From this we construct a non-trivially associated tensor …

We study noncommutative differential structures on the group of permutations SN, defined
by conjugacy classes. The 2-cycles class defines an exterior algebra ΛN which is a super …

In this book the details of many calculations are provided for access to work in quantum
groups, algebraic differential calculus, noncommutative geometry, fuzzy physics, discrete …

This paper is devoted to constructing quasitriangular bialgebras (or Hopf algebras). The tool
we use is a new coproduct, we call it the unified coproduct, in the construction of which a …

We introduce a new 2-parameter family of sigma models exhibiting Poisson–Lie T-duality on
a quasitriangular Poisson–Lie group G. The models contain previously known models as …

The dissertation presents possibilities of applying noncommutative spacetimes description,
particularly kappa-deformed Minkowski spacetime and Drinfeld's deformation theory, as a …

We show that the double 𝒟 of the nontrivially associated tensor category constructed from
left coset representatives of a subgroup of a finite group X is a modular category. Also we …

In this paper, the notion of a twisted partial Hopf coaction is introduced. The conditions on
partial cocycles are established in order to construct partial crossed coproducts. Then the …