Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation [PDF]
Entropy, 2020 In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to
Frédéric Barbaresco
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On Square-Integrable Representations of A Lie Group of 4-Dimensional Standard Filiform Lie Algebra [PDF]
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2020 In this paper, we study irreducible unitary representations of a real standard filiform Lie group with dimension equals 4 with respect to its basis. To find this representations we apply the orbit method introduced by Kirillov. The corresponding orbit of
Edi Kurniadi
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A non-smooth continuous unitary representation of a Banach-Lie group [PDF]
, 2008 5 ...
Daniel Beltiţă, Karl‐Hermann Neeb
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Jean-Marie Souriau’s Symplectic Foliation Model of Sadi Carnot’s Thermodynamics [PDF]
EntropyThe explanation of thermodynamics through geometric models was initiated by seminal figures such as Carnot, Gibbs, Duhem, Reeb, and Carathéodory. Only recently, however, has the symplectic foliation model, introduced within the domain of geometric ...
Frédéric Barbaresco
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AIMS MathematicsThis paper presents a survey of a geometrically exact beam theory formulated within the framework of Lie groups, aimed at providing a mathematically consistent description of slender structures undergoing large displacements and rotations.
Simone Fiori
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The representation ring of a compact Lie group revisited
Commentarii Mathematici Helvetici, 1998 We describe a new construction of the induction homomorphism for representation rings of compact Lie groups: a homomorphism first defined by Graeme Segal. The idea is to first define the induction homomorphism for class functions, and then show that this map sends characters to characters.
Robert Oliver
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Wavelet transforms associated to a principal series representation of semisimple Lie groups, I [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1995 Let \(G\) be a locally compact Lie group and \(\pi\) a continuous representation of \(G\) on a Hilbert space \({\mathcal H}\). Let \({\mathcal H}_\infty\) denote the space of \(C^\infty\)-vectors in \({\mathcal H}\), endowed with a natural Sobolev-type topology, and \({\mathcal H}_{- \infty}\) the dual of \({\mathcal H}_\infty\) endowed with the strong
Takeshi Kawazoe
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On the Unitarized Adjoint Representation of a Semisimple Lie Group II [PDF]
Canadian Journal of Mathematics, 1977 Let G be a connected semisimple Lie group with Lie algebra . Lebesgue measure on is invariant under the adjoint action of G; and so there is a natural unitary representation TG of G on L2 given ...
Ronald L. Lipsman
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Manifold Contrastive Learning with Variational Lie Group Operators [PDF]
Trans. Mach. Learn. Res., 2023 Self-supervised learning of deep neural networks has become a prevalent paradigm for learning representations that transfer to a variety of downstream tasks. Similar to proposed models of the ventral stream of biological vision, it is observed that these
Kion Fallah +3 more
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Representation Theory of the Lie Group T3and Three Index Bessel Functions
, 2013 M. A. Pathan, Mohannad J. S. Shahwan
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