1. The extension problem for lie group homomorphisms
- Author
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Robert J. Fisher and H. Turner Laquer
- Subjects
homomorphism ,Simple Lie group ,complexification ,Adjoint representation ,Lie group ,Lie conformal algebra ,Graded Lie algebra ,Algebra ,Adjoint representation of a Lie algebra ,Representation of a Lie group ,Computational Theory and Mathematics ,Lie algebra ,invariant connection ,Geometry and Topology ,holonomy ,parallel section ,Ambrose-Singer theorem ,Analysis ,Mathematics - Abstract
The fact that Lie algebra homomorphisms can be extended to Lie group homomorphisms, provided the source is simply connected, is well-known. The situation in the non-simply connected case is less clear. In this paper, we show how ideas from differential geometry provide a unifying viewpoint about such extension problems. In particular, the holonomy bundle of a flat invariant connection plays a central role.
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