RT Journal Article
T1 Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras
A1 Campoamor Stursberg, Otto-Rudwig
A1 Latini, Danilo
A1 Marquette, Ian
A1 Zhang, Yao-Zhong
AB Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians and the constants of the motion generating a polynomial symmetry algebra is proposed. The case of the special linear Lie algebra sl(n) is discussed in detail, where an explicit basis for the commutant with respect to the Cartan subalgebra is obtained, and the order of the polynomial algebra is computed. It is further shown that, with an appropriate realization of sl(n), this provides an explicit connection with the generic superintegrable model on the (n − 1)-dimensional sphere S n−1 and the related Racah algebra R(n). In particular, we show explicitly how the models on the two-sphere and three-sphere and the associated symmetry algebras can be obtained from the quadratic and cubic polynomial algebras generated by the commutants defined in the enveloping algebra of sl(3) and sl(4), respectively. The construction is performed in the classical (or Poisson-Lie) context, where the Berezin bracket replaces the commutator.
PB IOP Publishing
SN 0305-4470
YR 2023
FD 2023
LK https://hdl.handle.net/20.500.14352/73032
UL https://hdl.handle.net/20.500.14352/73032
LA eng
DS Docta Complutense
RD 25 abr 2025