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Contractions of Realizations
(Springer Nature Singapore Pte Ltd., 2020)
The direct application of the parameterized linear transformations (contraction matrices) to the Lie vector fields that realize a Lie algebra leads to improper (zero operators) realizations. This can be avoided by the ...
Equivalence of Vector Field Realizations of Lie Algebras from the Lie Group Point of View
(Springer Nature Singapore Pte Ltd., 2018)
The equivalence of vector field realizations of Lie algebras is considered from the viewpoint of the Lie algebra and also from the corresponding (local) Lie group. It is shown that for some stages in the establishment of ...
Construction of representations of Poincaré group using Lie fields
(American Institute of Physics, 2018)
In this paper, we give an explicit construction of the unitary irreducible representations of the Poincaré groups in 2, 3, and 4 space-time dimensions on Hilbert spaces associated with the Schrödinger representation of the ...
Realizations of Galilei algebras
(Institute of Physics Publishing, 2016)
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and ...
Comparison of realizations of Lie algebras
(IOP Publishing, 2018)
The notion of equivalence of Lie algebra realizations is revisited and the quantities stable under the equivalence transformations are proposed. As a result we formulate a practical algorithm that allows to establish the ...
Differential Invariants and Realizations of the Deformed Smallest Galilei Algebra
(MAIK "Nauka/Interperiodica", 2018)
Deformations of the smallest Galilei algebra are constructed and deformed algebras are realized by Lie vector fields. For these realization bases of differential invariants and operators of invariant differentiation are ...