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Some of the next articles are maybe not open access.
Canadian Journal of Mathematics, 1994
AbstractThe heat kernel of an amenable Lie group satisfies either pt ~ exp(—ct1/3) or pt ~ t-a as t → ∞. We give a condition on the Lie algebra which characterizes the two cases.
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AbstractThe heat kernel of an amenable Lie group satisfies either pt ~ exp(—ct1/3) or pt ~ t-a as t → ∞. We give a condition on the Lie algebra which characterizes the two cases.
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2020
In this chapter, we recall some well-known results on Lie groups and Lie algebras. In particular, we discuss the third Lie theorem, the Ado theorem, and the Cartan semisimplicity criterion. Some important types of Lie algebras and Lie groups together with their important ideals and normal subgroups are discussed.
Valerii Berestovskii, Yurii Nikonorov
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In this chapter, we recall some well-known results on Lie groups and Lie algebras. In particular, we discuss the third Lie theorem, the Ado theorem, and the Cartan semisimplicity criterion. Some important types of Lie algebras and Lie groups together with their important ideals and normal subgroups are discussed.
Valerii Berestovskii, Yurii Nikonorov
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2004
In this crucial lecture we introduce the definition of the Lie algebra associated to a Lie group and its relation to that group. All three sections are logically necessary for what follows; §8.1 is essential. We use here a little more manifold theory: specifically, the differential of a map of manifolds is used in a fundamental way in §8.1, the notion ...
William Fulton, Joe Harris
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In this crucial lecture we introduce the definition of the Lie algebra associated to a Lie group and its relation to that group. All three sections are logically necessary for what follows; §8.1 is essential. We use here a little more manifold theory: specifically, the differential of a map of manifolds is used in a fundamental way in §8.1, the notion ...
William Fulton, Joe Harris
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2014
The relationship between Lie algebras and Lie groups is of great importance. Let the Lie algebra be g and the corresponding Lie group G. The relation is $$\displaystyle{ \text{Lie algebra}\qquad g \ni X_{i}\mathrm{\ \ }(i = 1,\ldots,r) }$$ (4.1) $$\displaystyle{ \text{Lie group}\qquad G \ni \exp \left (\sum _{i=1}^{r}\alpha _{ i}X_{i ...
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The relationship between Lie algebras and Lie groups is of great importance. Let the Lie algebra be g and the corresponding Lie group G. The relation is $$\displaystyle{ \text{Lie algebra}\qquad g \ni X_{i}\mathrm{\ \ }(i = 1,\ldots,r) }$$ (4.1) $$\displaystyle{ \text{Lie group}\qquad G \ni \exp \left (\sum _{i=1}^{r}\alpha _{ i}X_{i ...
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1976
As we pointed out in 6.2, there are exactly two simple real Lie algebras of dimension 3. These are: the algebra \( {{\mathfrak{g}}_{1}} = \mathfrak{s}\mathfrak{l}\left( {2,R} \right) \) of real matrices of the second order with zero trace and the algebra \( {{\mathfrak{g}}_{2}} = \mathfrak{s}\mathfrak{o} = \left( {3,R} \right) \) of real skew-symmetric
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As we pointed out in 6.2, there are exactly two simple real Lie algebras of dimension 3. These are: the algebra \( {{\mathfrak{g}}_{1}} = \mathfrak{s}\mathfrak{l}\left( {2,R} \right) \) of real matrices of the second order with zero trace and the algebra \( {{\mathfrak{g}}_{2}} = \mathfrak{s}\mathfrak{o} = \left( {3,R} \right) \) of real skew-symmetric
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Towards a Lie theory of locally convex groups
Japanese Journal of Mathematics, 2006Karl-Hermann Neeb
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Lie ∗-homomorphisms between Lie C∗-algebras and Lie ∗-derivations on Lie C∗-algebras
Journal of Mathematical Analysis and Applications, 2004Chun-Gil Park
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