q-deformed classical Lie algebras and their anyonic realization
M Frau, M A R-Monteiro, S Sciuto
All classical Lie algebras can be realized a la Schwinger (1965) in terms of fermionic oscillators. We show that the same can be done for their q-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two-dimensional lattice. The deformation parameter q is a phase related to the anyonic statistical parameter. A crucial role in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the undeformed ones. The entire procedure works even on one-dimensional chains; in such a case q can also be real.
arXiv:hep-th/9304108•Journal of Physics A Mathematical and General•Feb 7, 1994•9 citations