Number operator algebras and deformations of \(\varepsilon\)-Poisson algebras (Q5944760)

The concept of generalized \(\varepsilon\)-superalgebras and their properties were introduced by \textit{M. Scheunert} [J. Math. Phys. 20, 712--720 (1979; Zbl 0423.17003)]. The paper gives further algebraic studies of this algebra. In section 2, the author gives the basic definitions of \(\varepsilon\)-superalgebra, \(\varepsilon\)-modules and tensor products. In section 3, he introduces the number operator algebras (n.o.a's) and proves in Theorem 2 the existence of a deformation parameter \(h\) for n.o.a , but this does not give much for the structure of the quantum algebra. The new deformed algebra structure enables further applications of n.o.a. to be found.