https://doi.org/10.1140/epjc/s10052-021-08993-1
Regular Article – Theoretical Physics
Generalized spinning particles on 
in accord with the Bianchi classification
1
Tomsk Polytechnic University, Lenin Ave. 30, 634050, Tomsk, Russia
2
Tomsk State University of Control Systems and Radioelectronics, 634050, Tomsk, Russia
a galajin@tpu.ru, a.galajinsky@tusur.ru
Received:
7
December
2020
Accepted:
20
February
2021
Published online:
2
March
2021
Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of generalized spinning particles on , the internal degrees of freedom of which are represented by a 3-vector obeying the structure relations of a three-dimensional real Lie algebra. Extensions involving an external field of the Dirac monopole, or the motion on the group manifold of SU(2), or a scalar potential giving rise to two quadratic constants of the motion are discussed. A procedure how to build similar models, which rely upon real Lie algebras with dimensions 
, is elucidated.
© The Author(s) 2021
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