Poisson Structures on the Galilei Group

Abstract

The complete list of Poisson-Lie structures on 4-d Galilei group is presented.

CANONICAL AND LIE-ALGEBRAIC TWIST DEFORMATIONS OF Κ-Poincaré AND CONTRACTIONS TO Κ-Galilei ALGEBRAS

“…As in the case of relativistic symmetries, forκ = ∞ we get dual group to the Galilei algebra U ξ,κ (G), while for ξ = 0 we obtain dual partner for the algebra U κ,κ (G). Finally, one should also notice that in theκ → ∞ and ξ → 0 limits we get the wellknown κ-deformed Galilei group G κ (see [36]), while for κ → ∞ and ξ → 0 orκ → ∞, we obtain the quantum Galilei groups recovered in [37].…”

The Henon–Heiles system defined on Lie-algebraically deformed Galilei spacetime

“…2 It should be noted that in accordance with the Hopf-algebraic classification of all deformations of relativistic and nonrelativistic symmetries (see references [15], [16]), apart of canonical [12]- [14] space-time noncommutativity, there also exist Lie-algebraic [14]- [19] and quadratic [14], [19]- [21] type of quantum spaces.…”

The Henon--Heiles System Defined on Canonically Deformed Space-time

“…2 It should be noted that in accordance with the Hopf-algebraic classification of all deformations of relativistic and nonrelativistic symmetries (see references [13], [14]), apart of canonical [10]- [12] space-time noncommutativity, there also exist Lie-algebraic [12]- [17] and quadratic [12], [17]- [19] type of quantum spaces.…”