arXiv subjects

O. Arratia

Publications and source records attributed to O. Arratia.

6 recordsLinked to original sources

arXiv2002

Local representations of the (1+1) quantum extended Galilei algebra

We present the q-deformed counterpart of the local representations of the (1+1) extended Galilei group. These representations act on the space of wavefunctions defined in the space-time. As in the classical case the q-local representations are reducible and the condition of irreducibility is given by the q-Casimir equation that in the limit of the deformation parameter going to zero becomes the Schroedinger equation of a free particle.

math.QA↗

arXiv2001

Representations of Quantum Bicrossproduct Algebras

We present a method to construct induced representations of quantum algebras having the structure of bicrossproduct. We apply this procedure to some quantum kinematical algebras in (1+1)--dimensions with this kind of structure: null-plane quantum Poincare algebra, non-standard quantum Galilei algebra and quantum kappa Galilei algebra.

math.QA↗

arXiv2001

Induced Representations of Quantum Groups

In this paper we show how to construct explicitly induced representations for bicrossproduct Hopf algebras with abelian kernels starting from one-dimensional characters of the commutative sector. We introduce this technique by means of two concrete physical examples: two quantum deformations of the (1+1) Galilei algebra.

math.QA↗

arXiv2001

Elements of the theory of induced representations

We analyze the elements characterizing the theory of induced representations of Lie groups, in order to generalize it to quantum groups. We emphasize the geometric and algebraic aspects of the theory, because they are more suitable for generalization in the framework of Hopf algebras. As an example, we present the induced representations of a quantum deformation of the extended Galilei algebra in (1+1) dimensions.

math.QA↗

arXiv2000

Induced representations of quantum kinematical algebras

We construct the induced representations of the null-plane quantum Poincaré and quantum kappa Galilei algebras in (1+1) dimensions. The induction procedure makes use of the concept of module and is based on the existence of a pair of Hopf algebras with a nondegenerate pairing and dual bases.

math.QA↗

arXiv1996

Moyal Quantization and Group Theory

We deduce a kernel that allows the Moyal quantization of the cylinder (as phase space) by means of the Stratonovich-Weyl correspondence.

quant-ph↗