Quantum homogeneous spaces of connected Hopf algebras

Low Dimensional Cocommutative Connected Hopf Algebras

William M. Singer’s theory of extensions of connected Hopf algebras is used to give a complete list of the cocommutative connected Hopf algebras over a field of positive characteristic p which have vector space dimension less than or equal to p3. The theory shows that there are exactly two noncommutative non-primitively generated Hopf algebras on the list, one of which is the Hopf algebra corre...

Homogeneous Countable Connected Hausdorff Spaces

In 1925, P. Urysohn gave an example of a countable connected Hausdorff space [4]. Other examples have been contributed by R. Bing [l], M. Brown [2], and E. Hewitt [3]. Relatively few of the properties of such spaces have been examined. In this paper the question of homogeneity is studied. Theorem I shows that there exists a bihomogeneous countable connected Hausdorff space. Theorems II and III ...

Extension Theory for Connected Hopf Algebras

Quantum Homogeneous Spaces as Quantum Quotient Spaces

We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The quantum plane and the general quantum two-spheres are discussed in detail. 0. Introduction A homogeneous space X of a Lie group G may be always identified wit...

Hopf Algebras in Quantum Computation

In this thesis, we use string diagrams to study the theory of Hopf algebras in the context of Categorical Quantum Mechanics. First, we treat the theory of representations of a Hopf algebra diagrammatically. The category of representations of a quasitriangular Hopf algebra Rep(H) is a braided tensor category and can be understood as a process theory of particles in Topological Quantum theory. We...