Geodesic
On a classification of faithful representations of the Galilean Lie algebra on the polynomial ring in three variables
Filomat, Tome 37 (2023) no. 9, p. 2807

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DOI

We show a complete classification of faithful representations of the 2 + 1 space-times Galilean Lie algebra on the polynomial ring in three variables, where actions of the Galilean Lie algebra are given by derivations with coefficients of degree at most one. In particular, all such representations of the Galilean Lie algebra are explicitly constructed and classified by one parameter. In a more general setting we show that, with respect to a nonzero abelian ideal of a finite-dimensional Lie algebra, there is at most one such representation up to graded-equivalence.
DOI : 10.2298/FIL2309807W
Classification : 17B10, 17B66, 16W25
Keywords: Lie algebras, derivations, polynomial rings, the Galilean Lie algebra 
Liang Wu; Youjun Tan. On a classification of faithful representations of the Galilean Lie algebra on the polynomial ring in three variables. Filomat, Tome 37 (2023) no. 9, p. 2807 . doi: 10.2298/FIL2309807W
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     title = {On a classification of faithful representations of the {Galilean} {Lie} algebra on the polynomial ring in three variables},
     journal = {Filomat},
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     year = {2023},
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     doi = {10.2298/FIL2309807W},
     language = {en},
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