Commutator Representations of Covariant Differential Calculi on Quantum Groups

Details Commutator Representations of Covariant Differential Calculi on Quantum Groups Commutator Representations of Covariant Differential Calculi on Quantum Groups

2001-05-30

arxiv.org/abs/math/0105251v1

Mathematics

Quantum Algebra

LaTeX2e, 14 pages

Scientific paper

Let (G,d) be a first order differential *-calculus on a *-algebra A. We say that a pair (\pi,F) of a *-representation \pi of A on a dense domain D of a Hilbert space and a symmetric operator F on D gives a commutator representation of G if there exists a linear mapping t:G -> L(D) such that t(adb)=\pi(a)i[F,\pi(b)], a,b in A. Among others, it is shown that each left-covariant *-calculus G of a compact quantum group Hopf *-algebra A has a faithful commutator representation. For a class of bicovariant *-calculi on A there is a commutator representation such that F is the image of a central element of the quantum tangent space. If A is the Hopf *-algebra of the compact form of one of the quantum groups SL_q(n+1), O_q(n), Sp_q(2n) with real transcendental q, then this commutator representation is faithful. Keywords: Quantum Groups; Noncommuative Geometry; Differential Calculus

Affiliated with

Also associated with

No associations

Rating

Commutator Representations of Covariant Differential Calculi on Quantum Groups 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 Commutator Representations of Covariant Differential Calculi on Quantum Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Commutator Representations of Covariant Differential Calculi on Quantum Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-555405