RT info:eu-repo/semantics/article
T1 Cayley-Klein Poisson Homogeneous Spaces
A1 Herranz Zorrilla, Francisco José
A1 Ballesteros Castañeda, Ángel
A1 Gutiérrez Sagredo, Iván
A1 Santander Navarro, Mariano
K1 Quantum groups
K1 Grupos cuánticos
K1 Riemannian geometry
K1 Geometría de Riemann
AB The nine two-dimensional Cayley–Klein geometries are firstly reviewed by following a gradedcontraction approach. Each geometry is considered as a set of three symmetrical homogeneous spaces (of points and two kinds of lines), in such a manner that the graded contractionparameters determine their curvature and signature. Secondly, new Poisson homogeneousspaces are constructed by making use of certain Poisson–Lie structures on the corresponding motion groups. Therefore, the quantization of these spaces provides noncommutativeanalogues of the Cayley–Klein geometries. The kinematical interpretation for the semiRiemannian and pseudo-Riemannian Cayley–Klein geometries is emphasized, since they arejust Newtonian and Lorentzian spacetimes of constant curvature.
SN 1314-3247
YR 2019
FD 2019
LK http://uvadoc.uva.es/handle/10324/40883
UL http://uvadoc.uva.es/handle/10324/40883
LA eng
NO Geometry, Integrability and Quantization, 2019, vol. XX.  p. 161-183
NO Producción Científica
DS UVaDOC
RD 22-nov-2024