Noncommutative quantum analogs of constant curvature spaces

TL;DR

This paper develops noncommutative quantum analogs of constant curvature spaces using Cayley-Klein schemes, detailing low-dimensional cases and various quantum deformations with different contraction parameters.

Contribution

It introduces a comprehensive framework for quantum analogs of constant curvature spaces incorporating Cayley-Klein contractions and analyzes low-dimensional cases in detail.

Findings

Multiple quantum analogs of constant curvature spaces are constructed.

The framework includes various quantum deformations with different contraction parameters.

Explicit descriptions of low-dimensional quantum spaces are provided.

Abstract

The quantum N-dimensional orthogonal vector Cayley-Klein spaces with different combinations of quantum structure and Cayley-Klein scheme of contractions and analytical continuations are described for multipliers, which include the first and the second powers of contraction parameters in the transformation of deformation parameter. The noncommutative analogs of constant curvature spaces are introduced. The low dimensional spaces with N=3,4 are discussed in detail and all quantum analogs of the fibered spaces corresponding to nilpotent values of contraction parameters are given. As a result the wide variety of the quantum deformations are obtained.