In mathematics, the Atiyah algebroid, or Atiyah sequence, of a principal -bundle over a manifold , where is a Lie group, is the Lie algebroid of the gauge groupoid of . Explicitly, it is given by the following short exact sequence of vector bundles over : It is named after Michael Atiyah, who introduced the construction to study the existence theory of complex analytic connections. It plays a crucial example in the integrability of (transitive) Lie algebroids, and it has applications in gauge theory and geometric mechanics.
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| - Atiyah algebroid (en)
- 아티야 준군 (ko)
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| - In mathematics, the Atiyah algebroid, or Atiyah sequence, of a principal -bundle over a manifold , where is a Lie group, is the Lie algebroid of the gauge groupoid of . Explicitly, it is given by the following short exact sequence of vector bundles over : It is named after Michael Atiyah, who introduced the construction to study the existence theory of complex analytic connections. It plays a crucial example in the integrability of (transitive) Lie algebroids, and it has applications in gauge theory and geometric mechanics. (en)
- 미분기하학에서 아티야 준군(Atiyah準群, 영어: Atiyah groupoid)은 매끄러운 주다발에 대하여 표준적으로 대응되는 리 준군이다. 그 리 준대수를 아티야 리 준대수(Atiyah Lie準代數, 영어: Atiyah Lie groupoid)라고 한다. (ko)
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| - In mathematics, the Atiyah algebroid, or Atiyah sequence, of a principal -bundle over a manifold , where is a Lie group, is the Lie algebroid of the gauge groupoid of . Explicitly, it is given by the following short exact sequence of vector bundles over : It is named after Michael Atiyah, who introduced the construction to study the existence theory of complex analytic connections. It plays a crucial example in the integrability of (transitive) Lie algebroids, and it has applications in gauge theory and geometric mechanics. (en)
- 미분기하학에서 아티야 준군(Atiyah準群, 영어: Atiyah groupoid)은 매끄러운 주다발에 대하여 표준적으로 대응되는 리 준군이다. 그 리 준대수를 아티야 리 준대수(Atiyah Lie準代數, 영어: Atiyah Lie groupoid)라고 한다. (ko)
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