the paper deal with non-commutative geometry. the notion of quantumspheres was introduced by podles. here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.

The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.

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...

Attention is focused on quantum spaces of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. Each of these quantum spaces can be combined with its symmetry algebra to form a Hopf algebra. The Hopf structures on quantum space coordinates imply their translation. This article is devoted to t...

In the foundations of quantum mechanics and quantum computing, there is often a split between research using infinite dimensional structures and research using finite dimensional structures. On the one hand, in axiomatic quantum foundations there is often a focus on finite dimensional spaces and matrix mechanics (e.g. [1, 45, 23, 46, 5, 3, 8, 9, 10, 13, 27]), and the same is true for circuit ba...

The FRT quantum Euclidean spaces O N q are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant curvature spaces are introduced as a spheres in the quantum Cayley-Klein spaces. For N = 5 part of them are interpreted as the noncommutative analogs of (1+3) space-time...

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SUq(2) . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector...

Associated to the standard SUq(n) R-matrices, we introduce quantum spheres S q , projective quantum spaces CP n−1 q , and quantum Grassmann manifolds Gk(C n q ). These algebras are shown to be homogeneous spaces of standard quantum groups and are also quantum principle bundles in the sense of T. Brzeziński and S. Majid [1].