Results 231 to 240 of about 274,463 (263)
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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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A cognitive approach to lie detection: A meta‐analysis
Legal and Criminological Psychology, 2017Aldert Vrij +2 more
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An introduction to Lie group integrators – basics, new developments and applications
Journal of Computational Physics, 2014Elena Celledoni +2 more
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Cohomology of Lie superalgebras and their generalizations
Journal of Mathematical Physics, 1998M Scheunert, R B Zhang
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