## Fermionic and bosonic representations for an extended affine Lie
algebra

### Yun Gao, York

The Clifford (or Weyl) algebras have natural representations on the

exterior (or symmetric) algebras of polynomials over half of generators.

Those representations are also important in quantum and statistical

mechanics where the generators are interpreted as operators which create

or annihilate particles and satisfy Fermi (or Bose) statistics.

In this talk, I will present a model for the extended affine Lie algebra

over quantum tori via the fermionic (or bosonic) construction.