arXiv subjects

M. Santander

Publications and source records attributed to M. Santander.

111 records · Page 7Linked to original sources

arXiv1994

Cayley-Klein Lie Algebras and their Quantum Universal Enveloping Algebras

The N-dimensional Cayley-Klein scheme allows the simultaneous description of $3^N$ geometries (symmetric orthogonal homogeneous spaces) by means of a set of Lie algebras depending on $N$ real parameters. We present here a quantum deformation of the Lie algebras generating the groups of motion of the two and three dimensional Cayley-Klein geometries. This deformation (Hopf algebra structure) is presented in a compact form by using a formalism developed for the case of (quasi) free Lie algebras. Their quasitriangularity (i.e., the most usual way to study the associativity of their dual objects, the quantum groups) is also discussed.

hep-th↗

arXiv1993

Cayley-Klein Algebras as Graded Contractions of so(N+1)

We study $\Bbb Z_2^{\otimes N}$ graded contractions of the real compact simple Lie algebra $so(N+1)$, and we identify within them the Cayley-Klein algebras as a naturally distinguished subset.

hep-th↗

arXiv1993

4D Quantum Affine Algebras and Space--Time q-Symmetries

A global model of $q$-deformation for the quasi--orthogonal Lie algebras generating the groups of motions of the four--dimensional affine Cayley--Klein geometries is obtained starting from the three dimensional deformations. It is shown how the main algebraic classical properties of the CK systems can be implemented in the quantum case. Quantum deformed versions of either the space--time or space symmetry algebras (Poincaré (3+1), Galilei (3+1), 4D Euclidean as well as others) appear in this context as particular cases and several $q$-deformations for them are directly obtained.

hep-th↗