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Generalised killing spinors on three-dimensional Lie groups.

Diego Artacho1

  • 1Department of Mathematics, Imperial College London, London, UK.

Manuscripta Mathematica
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Summary
This summary is machine-generated.

This study classifies invariant generalised Killing spinors on 3D Lie groups, finding that a single non-trivial spinor implies all spinors are generalised Killing. This classification is independent of the chosen metric.

Keywords:
15A66 (Secondary)22E6053C27 (Primary )

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Area of Science:

  • Differential Geometry
  • Mathematical Physics
  • Spinor Analysis

Background:

  • Invariant generalised Killing spinors are crucial in theoretical physics and differential geometry.
  • Understanding their properties on Lie groups provides insights into geometric structures.

Purpose of the Study:

  • To provide a complete classification of invariant generalised Killing spinors on three-dimensional Lie groups.
  • To explore the implications of non-trivial invariant generalised Killing spinors.

Main Methods:

  • Classification of invariant generalised Killing spinors.
  • Analysis of spinor properties on Lie groups.
  • Investigation of eigenvalue structures.

Main Results:

  • A complete classification of invariant generalised Killing spinors on three-dimensional Lie groups is presented.
  • The existence of a non-trivial invariant generalised Killing spinor necessitates all invariant spinors being generalised Killing with the same endomorphism.
  • This classification is independent of the choice of left-invariant metric.

Conclusions:

  • The study establishes a fundamental classification for invariant generalised Killing spinors in a specific mathematical context.
  • It highlights a significant property linking the existence of one such spinor to the nature of all others.
  • The findings offer a basis for further exploration of homogeneous manifolds admitting these spinors.