On some representations of nilpotent Lie algebras and superalgebras

Mathematics – Representation Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

Let $G$ be a simply connected, nilpotent Lie group with Lie algebra $\gee$. The group $G$ acts on the dual space $\gee^*$ by the coadjoint action. %% which partitions $\gee^*$ into coadjoint orbits. By the orbit method of Kirillov, the simple unitary representations of $G$ are in bijective correspondence with the coadjoint orbits in $\gee^*$, which in turn are in bijective correspondence with the primitive ideals of the universal enveloping algebra of $\gee$. The number of simple $\gee$-modules which have a common eigenvector for a particular subalgebra of $\gee$ and are annihilated by a particular primitive ideal $I$ is shown by Benoist to depend on geometric properties of a certain subvariety of the coadjoint orbit corresponding to $I$. We determine the exact number of such modules when the coadjoint orbit is two-dimensional. Bell and Musson showed that the algebras obtained by factoring the universal enveloping superalgebra of a Lie superalgebra by graded-primitive ideals are isomorphic to tensor products of Weyl algebras and Clifford algebras. We describe certain cases where the factors are purely Weyl algebras and determine how the sizes of these Weyl algebras depend on the graded-primitive ideals.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On some representations of nilpotent Lie algebras and superalgebras 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 On some representations of nilpotent Lie algebras and superalgebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On some representations of nilpotent Lie algebras and superalgebras will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-631334

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.