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Title of Journal: J Geom

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Abbravation: Journal of Geometry

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Springer Basel

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DOI

10.1001/jama.295.12.1434

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1420-8997

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On compact semisimple Lie groups as 2plectic mani

Authors: Mohammad Shafiee
Publish Date: 2014/04/21
Volume: 105, Issue: 3, Pages: 615-623
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Abstract

In this paper a compact and semisimple Lie group G is considered endowed with a 2plectic structure ω induced by the Killing form We show that the Lie group of 2plectomorphisms of G is finite dimensional and compact and hence the Darboux’s theorem fails to be true for this 2plectic structure Also it is shown that ω induces a leftinvariant mathfrakg valued 2form which is proportional to dΘ where Θ is the Cartan–Maurer 1form on G At last we consider the action of G on its tangent bundle which is furnished with the 2plectic structure ω c the complete lift of ω and calculate covariant momentum map of this action

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Other Papers In This Journal:
  1. A New Class of Translation Planes Constructed by Hyper-regulus Replacement
  2. Propellers in Affine Cayley–Klein Planes
  3. On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds
  4. Deformation of minimal surfaces with planar curvature lines
  5. Rakić duality principle in the almost Hermitian geometry
  6. An axiomatic look at the Erdős-Trost problem
  7. An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion
  8. Linearly small elation quadrangles
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