De Rham Cohomology and Hodge decomposition for Quantum Groups

Details De Rham Cohomology and Hodge decomposition for Quantum Groups De Rham Cohomology and Hodge decomposition for Quantum Groups

2000-08-25

arxiv.org/abs/math/0008195v1

Mathematics

Quantum Algebra

LaTeX2e, 40 pages

Scientific paper

Let G=G(t,z) be one of the N^2-dimensional bicovariant first order differential calculi for the quantum groups GL_q(N), SL_q(N), O_q(N), or Sp_q(N), where q is a transcendental complex number and z is a regular parameter. It is shown that the de Rham cohomology of Woronowicz' external algebra G^ coincides with the de Rham cohomologies of its left-coinvariant, its right-coinvariant and its (twosided) coinvariant subcomplexes. In the cases GL_q(N) and SL_q(N) the cohomology ring is isomorphic to the coinvariant external algebra G^_{inv} and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. Keywords: quantum groups, bicovariant differential calculi, de Rham cohomology, Laplace-Beltrami operator, Hodge theory

Affiliated with

Also associated with

No associations

Rating

De Rham Cohomology and Hodge decomposition for 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 De Rham Cohomology and Hodge decomposition for Quantum Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and De Rham Cohomology and Hodge decomposition for Quantum Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-433768