This work intends to present a study on relations between a Lie algebra
called dispersion operators algebra, linear canonical transformation and a
phase space representation of quantum mechanics that we have introduced and
studied in previous works. The paper begins with a brief recall of our previous
works followed by the description of the dispersion operators algebra which is
performed in the framework of the phase space representation. Then, linear
canonical transformations are introduced and linked with this algebra. A
multidimensional generalization of the obtained results is givenComment: 13 page
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