Abstract:
 We establish a noncommutative analogue of the first fundamental theorem of classical invariant theory. For a quantum group associated with each classical Lie algebra, we construct a noncommutative associative algebra
that admits an action of the quantum group. The subspace of invariants is shown to form a subalgebra, which is finitely generated. We construct the generators of the subalgebra of invariants and determine their commutation
relations. In the limit $q\rightarrow 1$, the results recover the first fundamental theorem of classical invariant theory. This is joint work with Gus Lehrer and H. Zhang.
