학술저널
ALGEBRAIC STRUCTURES IN A PRINCIPAL FIBRE BUNDLE
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 21, No. 3
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2008.09371 - 376 (6 pages)
- 0
Let P(M,G, ) =: P be a principal fibre bundle with structure Lie group G over a base manifold M. In this paper we get the following facts: 1. The tangent bundle TG of the structure Lie group G in P(M,G, ) =: P is a Lie group. 2. The Lie algebra g = TeG is a normal subgroup of the Lie group TG. 3. TP(TM, TG, ) =: TP is a principal fibre bundle with structure Lie group TG and projection over base manifold TM, where is the differential map of the projection of P onto M. 4. for a Lie group H, TH = H TeH = TeH H = TH and H \ TeH = {e}, but H is not a normal subgroup of the group TH in general.
1. Introduction
2. The proof of main results
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