Results 221 to 230 of about 467,532 (268)
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2017
New digital technologies have radically transformed the face of journalism in general and photo journalism in particular. These new technologies have not only made it easy for photo journalists to obtain images and to transmit them quickly to newsrooms and consumers across the globe, but they have also provided limitless opportunities for photo ...
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New digital technologies have radically transformed the face of journalism in general and photo journalism in particular. These new technologies have not only made it easy for photo journalists to obtain images and to transmit them quickly to newsrooms and consumers across the globe, but they have also provided limitless opportunities for photo ...
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1989
There are some things we take for granted which make the day-today business of living possible. One of them is telling the truth. No one would be so naive as to suppose that lies, white and otherwise, are not told from time to time, but we must have some basic ground rules whereby we can expect to be dealing with the truth, until we have reason to ...
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There are some things we take for granted which make the day-today business of living possible. One of them is telling the truth. No one would be so naive as to suppose that lies, white and otherwise, are not told from time to time, but we must have some basic ground rules whereby we can expect to be dealing with the truth, until we have reason to ...
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Lie superbialgebras and poisson-lie supergroups
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1993The basic notions of Lie bialgebras, Manin triples and classical Yang- Baxter equations are generalized to the case of Lie superalgebras. A class of Poisson-Lie supergroups is introduced. A rigorous formulation for a problem of quantization of Poisson supermanifolds is given.
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Quantization of Lie Groups and Lie Algebras
1988Publisher Summary This chapter focuses on the quantization of lie groups and lie algebras. The Algebraic Bethe Ansatz—the quantum inverse scattering method—emerges as a natural development of the various directions in mathematical physics: the inverse scattering method for solving nonlinear equations of evolution, the quantum theory of magnets, the ...
N. YU. RESHETIKHIN +2 more
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Journal of Lie Theory, 1994
This concisely written paper combines a survey of the standard facts about the structure of locally compact groups and their approximation by Lie groups with an exposition of the resulting structural similarities between locally compact groups of finite dimension and Lie groups.
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This concisely written paper combines a survey of the standard facts about the structure of locally compact groups and their approximation by Lie groups with an exposition of the resulting structural similarities between locally compact groups of finite dimension and Lie groups.
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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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