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Lie Algebras

Chia sẻ: Nguyễn Văn D D | Ngày: | Loại File: PDF | Số trang:198

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One of the important consequences of the mere existence of this formula is the following. Suppose that g is the Lie algebra of a Lie group G. Then the local structure of G near the identity, i.e. the rule for the product of two elements of G sufficiently closed to the identity is determined by its Lie algebra g. Indeed, the exponential map is locally a diffeomorphism from a neighborhood of the origin in g onto a neighborhood W of the identity, and if U ⊂ W is a (possibly smaller) neighborhood of the identity such that U · U ⊂ W, the the product of a...

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Nội dung Text: Lie Algebras

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