MPEJ Volume 7, No. 4, 59 pp.
Received: Mar 15, 2001. Revised: Oct 17, 2001. Accepted: Dec 12, 2001.

F. Besnard:
Number Operator Algebras

ABSTRACT: Under some hypotheses (symmetry, confluence), we enumerate
all quadratically presented algebras, generated by creation and
destruction operators, in which number operators exist. We show that
these are algebras of bosons, fermions, their immediate
generalizations that we call pseudo-bosons and pseudo-fermions, and
also matrix algebras, in the finitely generated case. We then recover
$q$-bosons (and pseudo-$q$-bosons) by a completion operation.

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