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Hom-Lie group and hom-Lie algebra from Lie group and Lie algebra perspective
International Journal of Geometric Methods in Modern Physics, 2021A hom-Lie group structure is a smooth group-like multiplication on a manifold, where the structure is twisted by a isomorphism. The notion of hom-Lie group was introduced by Jiang et al. as integration of hom-Lie algebra. In this paper we want to study hom-Lie group and hom-Lie algebra from the Lie group’s point of view. We show that some of important
Merati, S., Farhangdoost, M. R.
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Lie-Group and Lie-Algebra Inhomogenizations
Journal of Mathematical Physics, 1968A systematic formulation of the concept of inhomogenization is given both for Lie groups and for Lie algebras, and the connection between the two structures is clarified in terms of the notion of semidirect product. Special emphasis is devoted to the classification of the inhomogenizations of semisimple Lie algebras. As an application, a lemma due to O'
Berzi, V., Gorini, V.
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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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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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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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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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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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2021
In the last lecture, we introduced the description of rigid body motion in the three-dimensional world, including the rotation matrix, rotation vector, Euler angle, quaternion, and so on. We focused on the representation of rotation, but in SLAM, we have to estimate and optimize them in addition to the representation.
Xiang Gao, Tao Zhang
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In the last lecture, we introduced the description of rigid body motion in the three-dimensional world, including the rotation matrix, rotation vector, Euler angle, quaternion, and so on. We focused on the representation of rotation, but in SLAM, we have to estimate and optimize them in addition to the representation.
Xiang Gao, Tao Zhang
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