Construction of Simple q-Deformed Algebras by Statistics
S. U. Park
Abstract
The simple algebras of a dressed operator, which is composed of a dressing and a residual operators, are averaged following a proper statistics of the dressing one. In the Bose-Einstein statistics, a (fermionic) Calogero-Vasiliev oscillator, q-boson (fermion), and (fermionic) suq(1,1) are obtained for each bosonic (fermionic) residual operator. In the Fermi-Dirac statistics, new similar algebras are derived for each residual operator. Constructions of dual q-algebras, such as a dual Calogero-Vasiliev oscillator, a dual q-boson and a suq(2), and prospects are discussed.
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