## On the supersymmetry group of the classical Bose-Fermi oscillator.(English)Zbl 1136.81378

Summary: Applying the concept of a momentum map for supersymplectic supervectorspaces to the one-dimensional Bose-Fermi oscillator, we show that the largest symmetry group that admits a momentum map is the identity component of the intersection of the orthosymplectic group $$\text{OSp}(2|2)$$ and the group of supersymplectic transformations. This gives a systematic characterization of a certain class of odd supersymmetry transformations that were originally introduced in an ad hoc way.

### MSC:

 81Q60 Supersymmetry and quantum mechanics 81R05 Finite-dimensional groups and algebras motivated by physics and their representations