1.

Casimir operators of centrally extended l conformal Galilei algebra
/ Galajinsky, Anton ; Masterov, Ivan
The full set of Casimir elements of the centrally extended l conformal Galilei algebra is found in simple and tractable form..
Published in Nuclear Physics B (2019)
10.1016/j.nuclphysb.2019.114618
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2.

Eisenhart lift of 2dimensional mechanics
/ Fordy, Allan P. ; Galajinsky, Anton
The Eisenhart lift is a variant of geometrization of classical mechanics with d degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmanntype metric defined on (d+2) dimensional spacetime of Lorentzian signature. [...]
Published in EPJC 79 (2019) 301
10.1140/epjc/s1005201968126
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3.

Spinning extensions of D (2, 1; α ) superconformal mechanics
/ Galajinsky, Anton ; Lechtenfeld, Olaf
As is known, any realization of SU(2) in the phase space of a dynamical system can be generalized to accommodate the exceptional supergroup D (2, 1; α ), which is the most general N $$ \mathcal{N} $$ = 4 supersymmetric extension of the conformal group in one spatial dimension. [...]
Published in JHEP 1903 (2019) 069
10.1007/JHEP03(2019)069
arXiv:1902.06851
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4.

A variant of Schwarzian mechanics
/ Galajinsky, Anton
The Schwarzian derivative is invariant under SL(2,R) transformations and, as thus, any function of it can be used to determine the equation of motion or the Lagrangian density of a higher derivative SL(2,R) invariant 1 d mechanics or the Schwarzian mechanics for short. [...]
Published in Nuclear Physics B 936 (2018) 661667
10.1016/j.nuclphysb.2018.10.004
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5.

RuijsenaarsSchneider threebody models with N = 2 supersymmetry
/ Galajinsky, Anton
The RuijsenaarsSchneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. [...]
Published in JHEP 1804 (2018) 079
10.1007/JHEP04(2018)079
arXiv:1802.08011
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6.

Geometry of the isotropic oscillator driven by the conformal mode
/ Galajinsky, Anton
Geometrization of a Lagrangian conservative system typically amounts to reformulating its equations of motion as the geodesic equations in a properly chosen curved spacetime. [...]
Published in EPJC 78 (2018) 72
10.1140/epjc/s1005201855688
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7.

N =4 ℓ conformal Galilei superalgebras inspired by D (2 , 1; α ) supermultiplets
/ Galajinsky, Anton ; Krivonos, Sergey
N = 4 supersymmetric extensions of the ℓ conformal Galilei algebra are constructed by properly extending the Lie superalgebra associated with the most general N = 4 superconformal group in one dimension D (2 , 1; α ). [...]
Published in JHEP 1709 (2017) 131
10.1007/JHEP09(2017)131
arXiv:1706.08300
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8.

N = 4 l conformal Galilei superalgebra
/ Galajinsky, Anton ; Masterov, Ivan
An N=4 supersymmetric extension of the l conformal Galilei algebra is constructed. [...]
Published in Physics letters B (2017)
10.1016/j.physletb.2017.05.086
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9.

Couplings in D (2 , 1; α) superconformal mechanics from the SU(2) perspective
/ Galajinsky, Anton
Dynamical realizations of the most general N = 4 superconformal group in one dimension D (2 , 1; α ) are reconsidered from the perspective of the R symmetry subgroup SU(2). [...]
Published in JHEP 1703 (2017) 054
10.1007/JHEP03(2017)054
arXiv:1702.01955
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10.

Eisenhart lift for higher derivative systems
/ Galajinsky, Anton ; Masterov, Ivan
The Eisenhart lift provides an elegant geometric description of a dynamical system of second order in terms of null geodesics of the Brinkmanntype metric. [...]
Published in Physics letters B (2016)
10.1016/j.physletb.2016.11.059
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