Abstract
It is well known that the Lie algebra structure on quantum algebras gives rise to a Poisson algebra structure on classical algebras as the Planck constant goes to 0. We show that this correspondence still holds in the generalization of superalgebra introduced by Scheunert, called ε-algebra. We illustrate this with the example of Number Operator Algebras, a new kind of object that we have defined and classified under some assumptions.
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Besnard, F. Number Operator Algebras and Deformations of ε-Poisson Algebras. Letters in Mathematical Physics 55, 113–125 (2001). https://doi.org/10.1023/A:1010907630787
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DOI: https://doi.org/10.1023/A:1010907630787