The Structure Of Q - Deformed Virasoro Algebra

In [1], H. Hiro-oka,O. Matsui, T. Naito and S. Saito introduced and studied the g-deformation Virasoro algebra (?)q in1990. It is an infinite dimensional Lie algebra with a basis{Lmα m∈Z, α∈Z+} and the Lie bracket [-,-] defined by where q E C (q≠0,±1),[m]q=(qm-q-m)/(q-q-1), andIn this thesis, we study the algebraic structure of the Lie algebra Cq. Our main results are as follows:1) We show that Cq is a finitely generated perfect Lie algebra.2) We classify all invariant symmetric bilinear forms on Cq: where3) We compute the first cohomology of Cq with coefficients in the adjoint module: where4) We determine the second cohomology of Cq with coefficients in the trivial mod-ule: where5) We determine the universal central extension of (?)q: with...