scholarly journals Dynamical realization of l-conformal Galilei algebra and oscillators

2013 ◽  
Vol 866 (2) ◽  
pp. 212-227 ◽  
Author(s):  
Anton Galajinsky ◽  
Ivan Masterov
Keyword(s):  
Dynamical Realization ◽  
Galilei Algebra

scholarly journals On deformations of the Galilei algebra

2021 ◽  
Vol 2090 (1) ◽  
pp. 012066
Author(s):  
María Alejandra Alvarez ◽  
Javier Rosales-Gómez
Keyword(s):  
Lie Algebra ◽  
Galilei Algebra

Abstract In this note we compute all deformations of the 4-dimensional classical Galilei algebra &. In particular, we find examples of quadratic, cubic and quartic Lie algebra deformations.

Two Dimensional Cayley-Klein Algebras Generated by Expansions

1997 ◽  
Vol 12 (01) ◽  
pp. 259-264 ◽  
Author(s):  
L. M. Nieto ◽  
J. Negro ◽  
M. Santander
Keyword(s):  
Lie Algebras ◽  
Two Dimensional ◽  
Galilei Algebra

Expansion methods are applied in order to get extended two dimensional Cayley-Klein Lie algebras. The keystone of the construction will be the two dimensional extended Galilei algebra whose generators are used to define, by means of formal functions, generators closing any of the nine two-dimensional extended Cayley-Klein Lie algebras.

scholarly journals New realizations of 𝒩 = 2l-conformal Newton–Hooke superalgebra

2015 ◽  
Vol 30 (13) ◽  
pp. 1550073 ◽  
Author(s):  
Ivan Masterov
Keyword(s):  
Cosmological Constant ◽  
Differential Operators ◽  
Linear Differential Operators ◽  
Negative Cosmological Constant ◽  
Linear Differential ◽  
Math Phys ◽  
Dynamical Realization

By applying Niederer-like transformation, we construct a representation of the 𝒩 = 2l-conformal Newton–Hooke (NH) superalgebra for the case of a negative cosmological constant in terms of linear differential operators as well as its dynamical realization. Another variant of 𝒩 = 2 supersymmetric Pais–Uhlenbeck oscillator for a particular choice of its frequencies is proposed. The advantages of such realizations as compared to their analogues introduced in [I. Masterov, J. Math. Phys.53, 072904 (2012)], are discussed.

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