Anyonic Realization of $S{U}_q(N)$ Quantum Algebra

Abstract

By considering a set of $N$ anyonic oscillators ( non-local, intrinsic two-dimensional objects interpolating between fermionic and bosonic oscillators) on a two-dimensional lattice, we realize the $S{U}_q(N)$ quantum algebra by means of a generalized Schwinger construction. We find that the deformation parameter $q$ of the algebra is related to the anyonic statistical parameter $\nu$ by $q=exp(\mathrm{i}\pi \nu )$.

12 pages, DFTT 5/93

References in corpus (2)

• An introduction to non-commutative differential geometry on quantum groups
• Anyons and Quantum Groups

Cited by in corpus (6)

• Anyons and Quantum Groups
• Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N)
• Slave Anyons in the $t$-$J$ Model at the Supersymmetric Point
• $q$-Deformed Classical Lie Algebras and their Anyonic Realization
• On the Class of Possible Nonlocal Anyon-Like Operators and Quantum Groups
• Multiparameter Deformations of the Algebra $g{l}_n$ in Terms of Anyonic Oscillators