• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.207-212
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• 2024

In this paper, we study Malcev algebra bundles and Malcev algebra bundles of finite type. Lie algebra bundles and Lie transformation algebra bundles are defined using given Malcev algebra bundle and we conclude some results for finite type.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.371-376
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• 2008

Let $P(M,G,{\pi})=:P$ 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 $P(M,G,{\pi})=:P$ is a Lie group. 2. The Lie algebra ${\mathcal{g}}=T_eG$ is a normal subgroup of the Lie group TG. 3. $TP(TM,TG,{\pi}_*)=:TP$ is a principal fibre bundle with structure Lie group TG and projection ${\pi}_*$ over base manifold TM, where ${\pi}_*$ is the differential map of the projection ${\pi}$ of P onto M. 4. for a Lie group $H,\;TH=H{\circ}T_eH=T_eH{\circ}H=TH$ and $H{\cap}T_eH=\{e\}$, but H is not a normal subgroup of the group TH in general.