A Class Of Noether Modules For Quantum Torus C_-1

Let C_-1be the quantum torus Lie algebra C_-1 with q=1. Using the Laurentpolynomial ring[x^±1]as representation space, we construct a class of modules, over theC_-1, which are Noether modules but not Artin modules. Then we determine all of theirsubmodules and quotient modules and all the homomorphisms between these modules.Finally, we show the relationship between these modules and the faithful representations ofthe typeA₁loop algebra.