Linear Representation of Lie Group [PDF]
arXiv, 2010 In this book, I explored differential equations for operation in Lie group and for representations of group Lie in a vector space.
Aleks Kleyn
arxiv +5 more sources
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
doaj +2 more sources
Linking Lie groupoid representations and representations of infinite-dimensional Lie groups [PDF]
Ann Glob Anal Geom (2019) 55 Issue 4, pp 749-775, 2018 The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged here are the bisection group and a group of groupoid self maps.
Habib Amiri, Alexander Schmeding
arxiv +5 more sources
A type B analog of the Lie representation [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We describe a type B analog of the much studied Lie representation of the symmetric group. The nth Lie representation of Sn restricts to the regular representation of Sn−1, and our generalization mimics this property.
Andrew Berget
doaj +1 more source
The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras
Electronic Research Archive, 2022 The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploits strongly the Hom-type structure and fits perfectly with simultaneous deformations of
Shanshan Liu +2 more
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Surjektifitas Pemetaan Eksponensial untuk Grup Lie Heisenberg yang Diperumum
Jambura Journal of Mathematics, 2023 The Heisenberg Lie Group is the most frequently used model for studying the representation theory of Lie groups. This Lie group is modular-noncompact and its Lie algebra is nilpotent.
Edi Kurniadi +2 more
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Ruang Fase Tereduksi Grup Lie Aff (1)
Jambura Journal of Mathematics, 2021 ABSTRAK Dalam artikel ini dipelajari ruang fase tereduksi dari suatu grup Lie khususnya untuk grup Lie affine berdimensi 2. Tujuannya adalah untuk mengidentifikasi ruang fase tereduksi dari melalui orbit coadjoint buka di titik tertentu pada ruang ...
Edi Kurniadi
doaj +1 more source
Generalized Reynolds Operators on Lie-Yamaguti Algebras
Axioms, 2023 In this paper, the notion of generalized Reynolds operators on Lie-Yamaguti algebras is introduced, and the cohomology of a generalized Reynolds operator is established.
Wen Teng, Jiulin Jin, Fengshan Long
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SCENE CLASSIFICATION BASED ON THE INTRINSIC MEAN OF LIE GROUP [PDF]
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2020 Remote Sensing scene classification aims to identify semantic objects with similar characteristics from high resolution images. Even though existing methods have achieved satisfactory performance, the features used for classification modeling are still ...
C. Xu, G. Zhu, K. Yang
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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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