| In this thesis, we investigate the problem of quantizing the Witt algebra and its representations over complex number field.;In chapter 1, we begin by introducing the quantum Witt algebra, the quantum Virasoro algebra and a q-analogue of the simplest affine Kac-Moody algebra ;In chapter 2, after introducing quantum flexible algebras, we prove that q-analogues of the two characterizations of the usual Witt algebra hold for the quantum Witt algebra.;In chapter 3, we give our quantization of the enveloping algebra of the Witt algebra; construct the q-analogues of the module of tensor fields over the Witt algebra; study their properties and prove a q-analogue of Kaplansky's theorem concerning the module of tensor fields over the Witt algebra. |
