RT Journal Article
T1 Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras
A1 Campoamor Stursberg, Otto Ruttwig
A1 Marquette, Ian
AB We discuss a procedure to determine finite sets M within the commutant of an algebraic Hamiltonian in the enveloping algebra of a Lie algebra g such that their generators define a quadratic algebra. Although independent from any realization of Lie algebras by differential operators, the method is partially based on an analytical approach, and uses the coadjoint representation of the Lie algebra g. The procedure, valid for non-semisimple algebras, is tested for the centrally extended Schrödinger algebras Ŝ(n) for various different choices of algebraic Hamiltonian. For the so-called extended Cartan solvable case, it is shown how the existence of minimal quadratic algebras can be inferred without explicitly manipulating the enveloping algebra.
PB Elsevier Masson
SN 0003-4916
YR 2022
FD 2022-02
LK https://hdl.handle.net/20.500.14352/71836
UL https://hdl.handle.net/20.500.14352/71836
LA eng
NO Ministerio de Ciencia e Innovación (MICINN)/FEDER
DS Docta Complutense
RD 4 may 2024