The space of m-ary differential operators as a module over the Lie algebra of vector fields

Details The space of m-ary differential operators as a module over the Lie algebra of vector fields The space of m-ary differential operators as a module over the Lie algebra of vector fields

2006-03-13

arxiv.org/abs/math/0603287v2

Journal of Geom. Phys. 57, no. 6, (2007), 1441-1456

Mathematics

Quantum Algebra

20 pages; LaTeX2e; minor corrections

Scientific paper

10.1016/j.geomphys.2006.12.002

The space of m-ary differential operators acting on weighted densities is a (m+1)-parameter family of modules over the Lie algebra of vector fields. For almost all the parameters, we construct a canonical isomorphism between this space and the corresponding space of symbols as sl(2)-modules. This yields to the notion of the sl(2)-equivariant symbol calculus for m-ary differential operators. We show, however, that these two modules cannot be isomorphic as sl(2)-modules for some particular values of the parameters. Furthermore, we use the symbol map to show that all modules of second-order m-ary differential operators are isomorphic to each other, except for few modules called singular.

Affiliated with

Also associated with

No associations

Rating

The space of m-ary differential operators as a module over the Lie algebra of vector fields 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 The space of m-ary differential operators as a module over the Lie algebra of vector fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The space of m-ary differential operators as a module over the Lie algebra of vector fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-69599