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SIAM Journal on Numerical Analysis, 1999
The author discusses variants of Hermite interpolation in Lie group. He also considers continuous extensions to some of the new geometric integration methods by equipping them with continuous weights.
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The author discusses variants of Hermite interpolation in Lie group. He also considers continuous extensions to some of the new geometric integration methods by equipping them with continuous weights.
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The Automorphism Group of a Lie Group
Transactions of the American Mathematical Society, 1952Introduction. The group A (G) of all continuous and open automorphisms of a locally compact topological group G may be regarded as a topological group, the topology being defined in the usual fashion from the compact and the open subsets of G (see ?1). In general, this topological structure of A (G) is somewhat pathological.
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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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Groups, Lie Groups, and Lie Algebras
2011This chapter introduces abstract groups and Lie groups, which are a formalization of the notion of a physical transformation. The chapter begins with a heuristic introduction that motivates the definition of a group and gives an intuitive sense for what an “infinitesimal generator” is.
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Journal of Mathematical Physics, 1961
Contraction is defined for a Lie group to coincide on its Lie algebra with a generalization of contraction as first introduced by Inönü and Wigner. This is accomplished with a sequence of nonsingular coordinate transformations on the group (or nonsingular linear coordinate transformations on its Lie algebra), whose limit is a singular one.
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Contraction is defined for a Lie group to coincide on its Lie algebra with a generalization of contraction as first introduced by Inönü and Wigner. This is accomplished with a sequence of nonsingular coordinate transformations on the group (or nonsingular linear coordinate transformations on its Lie algebra), whose limit is a singular one.
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Journal of Lie Theory, 1995
A connected Lie group \(G\) is called spacious if there exists an open subset \(U \subseteq G\) such that \(U^n \cap U^{n + 1} = \emptyset\) for all \(n \in N\). This property is closely related to the behaviour of the exponential function \(\text{exp} : g \to G\) because, according to a result of Jaworski, \(G\) is spacious if and only if \(\text{exp }
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A connected Lie group \(G\) is called spacious if there exists an open subset \(U \subseteq G\) such that \(U^n \cap U^{n + 1} = \emptyset\) for all \(n \in N\). This property is closely related to the behaviour of the exponential function \(\text{exp} : g \to G\) because, according to a result of Jaworski, \(G\) is spacious if and only if \(\text{exp }
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Journal of Lie Theory, 1995
Various notions of approximation of locally compact groups by Lie groups have been studied in the literature, and there are indications that there is some danger of confusion. Therefore, the author undertakes a systematic comparison. A Lie-normal family in a locally compact Hausdorff group \(G\) is defined as a set \({\mathcal N}\) of normal subgroups ...
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Various notions of approximation of locally compact groups by Lie groups have been studied in the literature, and there are indications that there is some danger of confusion. Therefore, the author undertakes a systematic comparison. A Lie-normal family in a locally compact Hausdorff group \(G\) is defined as a set \({\mathcal N}\) of normal subgroups ...
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On the tangent Lie group of a symplectic Lie group
Ricerche di Matematica, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Annals of Mathematics, 1947
where i a =-(2(ai)2)1/2 and where F satisfies the sole condition that F -O 0 as a -O 0, b 0. The coordinate system is right-regular if I b I replaces I a I in (1.1). A coordinate system a, *., at is analytic if the coordinates (ab)t of ab are expressible as power series in a', * , a, bl, * , bT which converge for some domain: I a I < 6, I b I < 6.
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where i a =-(2(ai)2)1/2 and where F satisfies the sole condition that F -O 0 as a -O 0, b 0. The coordinate system is right-regular if I b I replaces I a I in (1.1). A coordinate system a, *., at is analytic if the coordinates (ab)t of ab are expressible as power series in a', * , a, bl, * , bT which converge for some domain: I a I < 6, I b I < 6.
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