arXiv:1806.08406 Abstract | arXiv Analytics

arXiv:1806.08406 [math.RT]Abstract References Reviews Resources

A bijection between the adjoint and coadjoint orbits of a semidirect product

Published 2018-06-21Version 1

We prove that there exists a geometric bijection between the sets of adjoint and coadjoint orbits of a semidirect product, provided a similar bijection holds for particular subgroups. We also show that under certain conditions the homotopy types of any two orbits in bijection with each other are the same. We apply our theory to the examples of the affine group and the Poincar\'{e} group, and discuss the limitations and extent of this result to other groups.

Comments: 14 pages

Categories: math.RT, math.DG

Keywords: coadjoint orbits, semidirect product, similar bijection holds, affine group, homotopy types

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