  We initiate an algebraic approach to the many-anyon problem based on deformed
oscillator algebras. The formalism utilizes a generalization of the deformed
Heisenberg algebras underlying the operator solution of the Calogero problem.
We define a many-body Hamiltonian and an angular momentum operator which are
relevant for a linearized analysis in the statistical parameter nu. There
exists a unique ground state and, in spite of the presence of defect lines, the
anyonic weight lattices are completely connected by the application of the
oscillators of the algebra. This is achieved by supplementing the oscillator
algebra with a certain projector algebra.
