Results 201 to 210 of about 712 (260)
Coherent control of dark and bright spatio-temporal solitons of SPPs at a silver silica nano-composite interface with gain-assisted atomic medium. [PDF]
Sci RepElahi N +6 more
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Tunneling Splittings in the Water Hexamer Prisms Composed of Stacked Water Trimers. [PDF]
J Phys Chem ATokić N, Cvitaš MT.
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A ϱ -Weyl fractional operator of the extended S -type function in a complex domain. [PDF]
MethodsXHadi SH, Challab KA, Ali AH, Alatawi AA.
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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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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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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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Algebra, Lie Group and Lie Algebra
2010Geometry, algebra, and analysis are usually called the three main branches of mathematics. This chapter introduces some fundamental results in algebra that are mostly useful in systems and control. In section 4.1 some basic concepts of group and three homomorphism theorems are discussed. Ring and algebra are introduced briefly in section 4.2. As a tool,
Daizhan Cheng, Xiaoming Hu, Tielong Shen
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1985
In this chapter we explain what a Lie group is and quickly review the basic concepts of the theory of differentiable manifolds. The first section illustrates the notion of a Lie group with classical examples of matrix groups from linear algebra. The spinor groups are treated in a separate section, §6, but the presentation of the general theory of ...
Theodor Bröcker, Tammo tom Dieck
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In this chapter we explain what a Lie group is and quickly review the basic concepts of the theory of differentiable manifolds. The first section illustrates the notion of a Lie group with classical examples of matrix groups from linear algebra. The spinor groups are treated in a separate section, §6, but the presentation of the general theory of ...
Theodor Bröcker, Tammo tom Dieck
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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
openaire +1 more source