Results 11 to 20 of about 13,564,364 (338)
Baker–Campbell–Hausdorff–Dynkin Formula for the Lie Algebra of Rigid Body Displacements
Mathematics, 2020 The paper proposes, for the first time, a closed form of the Baker–Campbell–Hausdorff–Dynkin (BCHD) formula in the particular case of the Lie algebra of rigid body displacements.
Daniel Condurache, Ioan-Adrian Ciureanu
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Survey on Lie Group Machine Learning
Big Data Mining and Analytics, 2020 Lie group machine learning is recognized as the theoretical basis of brain intelligence, brain learning, higher machine learning, and higher artificial intelligence. Sample sets of Lie group matrices are widely available in practical applications.
Mei Lu, Fanzhang Li
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Geometry of Tangent Poisson–Lie Groups
Mathematics, 2023 Let G be a Poisson–Lie group equipped with a left invariant contravariant pseudo-Riemannian metric. There are many ways to lift the Poisson structure on G to the tangent bundle TG of G.
Ibrahim Al-Dayel +2 more
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Transactions of the American Mathematical Society, 1985 This paper studies the structure of locally compact groups which are determined by Lie groups in one form or another. The best understood class if that of pro-Lie groups G (which are locally compact groups with arbitrarily small compact normal subgroups N such that G/N is a Lie group. Theorem 1 says that these are precisely those groups G such that for
J. S. Yang, T. S. Wu, R. W. Bagley
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The Lie Group Structure of the Butcher Group [PDF]
Foundations of Computational Mathematics, 2014 The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge–Kutta methods. In the present paper, we complement the algebraic treatment of the Butcher group with a natural infinite ...
Geir Bogfjellmo, Alexander Schmeding
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On the Solution of the Schrödinger Equation with Position-Dependent Mass
Universe, 2020 We have considered the Iwasawa and Gauss decompositions for the Lie group SL(2,R). According to these decompositions, the Casimir operators of the group and the Hamiltonians with position-dependent mass were expressed.
Mehmet Sezgin
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Asian Journal of Mathematics, 2014 46 ...
Li-Bland, David, Meinrenken, Eckhard
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An example of a non-Borel locally-connected finite-dimensional topological group
Karpatsʹkì Matematičnì Publìkacìï, 2017 According to a classical theorem of Gleason and Montgomery, every finite-dimensional locally path-connected topological group is a Lie group. In the paper for every $n\ge 2$ we construct a locally connected subgroup $G\subset{\mathbb R}^{n+1}$ of ...
I.Ya. Banakh, T.O. Banakh, M.I. Vovk
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Michigan Mathematical Journal, 2004 For various series of complex semi-simple Lie algebras $\fg (t)$ equipped with irreducible representations $V(t)$, we decompose the tensor powers of $V(t)$ into irreducible factors in a uniform manner, using a tool we call {\it diagram induction}. In particular, we interpret the decompostion formulas of Deligne \cite{del} and Vogel \cite{vog} for ...
Landsberg, J. M., Manivel, L.
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Einstein warped product spaces on Lie groups
Cubo, 2022 We consider a compact Lie group with bi-invariant metric, coming from the Killing form. In this paper, we study Einstein warped product space, $M = M_1 \times_{f_1} M_2$ for the cases, $(i)$ $M_1$ is a Lie group $(ii)$ $M_2$ is a Lie group and $(iii ...
Buddhadev Pal +2 more
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