The Lie bialgebras of the (1+1) extended Galilei algebra are obtained and classified into four multiparametric families. Their quantum deformations are obtained, together with the corresponding deformed Casimir operators. For the coboundary cases quantum universal R-matrices are also given. Applications of the quantum extended Galilei algebras to classical integrable systems are explicitly deve...

A particular deformation of central extended Galilei group is considered. It is shown that the deformation influences the rules of constructing the composed systems while one particle states remain basically unaffected. In particular the mass appeared to be non additive.

Finite-dimensional nonrelativistic conformal Lie algebras spanned by polynomial vector fields of Galilei spacetime arise if the dynamical exponent is z = 2/N with N = 1, 2, . . . . Their underlying group structure and matrix representation are constructed (up to a covering) by means of the Veronese map of degree N . Suitable quotients of the conformal Galilei groups provide us with Newton-Hooke...

The noncommutative spacetimes associated to the κ-Poincaré relativistic symmetries and their “non-relativistic” (Galilei) “ultra-relativistic” (Carroll) limits are indistinguishable, since coordinates satisfy same algebra. In this work, we show that three quantum kinematical models can be differentiated when looking at spaces of time-like worldlines. Specifically, construct geodesics with κ-Gal...

The “Jackiw-Nair” non-relativistic limit of the relativistic anyon equations provides us with infinite-component wave equations of the Dirac-Majorana-Lévy-Leblond type for the “exotic” particle, associated with the two-fold central extension of the planar Galilei group. An infinite dimensional representation of the Galilei group is found. The velocity operator is studied, and the observable coo...

A classification of all possible realizations of the Galilei, Galilei-similitude and Schrödinger Lie algebras in three dimensional space-time in terms of vector fields under the action of the group of local diffeomorphisms of the space R3 × C is presented. Using this result a variety of general second order evolution equations invariant under the corresponding groups are constructed and their p...

A general method to easily build global and relative operators for any number n of elementary systems if they are defined for 2 is presented. It is based on properties of the morphisms valued in the tensor products of algebras of the kinematics and it allows also the generalization to any n of relations demonstrated for two. The coalgebra structures play a peculiar role in the explicit construc...