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
On the Differentability of the Unitary Representation of the Lie Group. [PDF]
, 1951 J. von Neumann ([2]) has introduced the notion of the differentiablity of the matric group, and given a method of forming Lie algebras of matric Lie groups. This notion was extended further by K. Yosida ([4]) to the group embedded in tne normed ring.
Jyun-ichi HANO
openalex +2 more sources
Representation Theory of the Lie Group T3and Three Index Bessel Functions
, 2013 The theory of generalized Bessel functions is reformulated within the framework of an operational formalism using the multiplier representation of the Lie group as suggested by Miller.
M. A. Pathan, Mohannad J. S. Shahwan
openalex +3 more sources
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
semanticscholar +1 more source
Error bounds for Lie group representations in quantum mechanics [PDF]
Journal of Physics A: Mathematical and Theoretical, 2022 We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian ...
Lauritz van Luijk +3 more
semanticscholar +1 more source
Nonlinear Filter for Simultaneous Localization and Mapping on a Matrix Lie Group Using IMU and Feature Measurements [PDF]
IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021 Simultaneous localization and mapping (SLAM) is a process of concurrent estimation of the vehicle’s pose and feature locations with respect to a frame of reference.
Hashim A. Hashim, A. E. Eltoukhy
semanticscholar +1 more source
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
A new division algebra representation of E8 [PDF]
Journal of Mathematics and Physics, 2023 We construct the well-known decomposition of the Lie algebra e8 into representations of e6⊕su(3) using explicit matrix representations over pairs of division algebras.
T. Dray, C. Manogue, Robert A. Wilson
semanticscholar +1 more source