A quantum analogue of the first fundamental theorem of invariant theory

Details A quantum analogue of the first fundamental theorem of invariant theory A quantum analogue of the first fundamental theorem of invariant theory

2009-08-11

arxiv.org/abs/0908.1425v1

Mathematics

Quantum Algebra

44 pages, 3 figures

Scientific paper

We establish a noncommutative analogue of the first fundamental theorem of classical invariant theory. For each quantum group associated with a classical Lie algebra, we construct a noncommutative associative algebra whose underlying vector space forms a module for the quantum group and whose algebraic structure is preserved by the quantum group action. The subspace of invariants is shown to form a subalgebra, which is finitely generated. We determine generators of this subalgebra of invariants and determine their commutation relations. In each case considered, the noncommutative modules we construct are flat deformations of their classical commutative analogues. Thus by taking the limit as $q\to 1$, our results imply the first fundamental theorem of classical invariant theory, and therefore generalise them to the noncommutative case.

Affiliated with

Also associated with

No associations

Rating

A quantum analogue of the first fundamental theorem of invariant theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A quantum analogue of the first fundamental theorem of invariant theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A quantum analogue of the first fundamental theorem of invariant theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-164127