Lie Groups

By Kyungyong Lee, Frank Raymond

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Luc Van Gool
2. Zhiwu Huang
3. J. Heckman
4. Hossein Rahmani
5. M. Del Zotto
6. Percy Liang
7. C. Vafa
8. Jun Liu

Citations in the corpus

• Deep Learning on Lie Groups for Skeleton-Based Action Recognition (2016, background): “The set of n×n rotation matrices in R forms the special orthogonal group SOn which is actually a matrix Lie group [22, 9, 16].”
• Discriminative virtual views for cross-view action recognition (2012, background): “More details on SO(D) can be found, for example, in [12].”
• Higher-order interference and single-system postulates characterizing quantum theory (2014, background): “According to [20] and [21], the only compact connected Lie group which acts transitively and effectively on it is the exceptional Lie group F4.”
• Moment Maps, Cobordisms, and Hamiltonian Group Actions (2002, methodology): “We encourage the reader to also consult the book [DK] by Duistermaat and Kolk.”
• Linear growth of quantum circuit complexity (2021, background): “Both are locally invertible in small neighbourhoods around x and U by a standard result in Lie group theory [26].”
• Hopf saddle-node bifurcation for fixed points of 3D-diffeomorphisms: Analysis of a resonance ‘bubble’ (2008, unknown): “Since Y1 commutes with Y2, the time-γ map of Yγ,μ,ω is given by the composition of the time-γ maps Y γ 1 and Y γ 2 (this is a corollary of the Baker–Campbell–Hausdorff formula [65]).”
• Asymptotic expansion of the heat kernel for orbifolds (2008, methodology): “As discussed in [14], the orbit space of a proper Lie group action on a smooth manifold has this property.”
• Geometric Means in a Novel Vector Space Structure on Symmetric Positive-Definite Matrices (2007, background): “Remarkably, this deviation can be expressed only in terms of Lie brackets between M and N [14].”
• Combinatorial Commutative Algebra (2004, methodology): “From there, Gelfand–Tsetlin patterns lead to symplectic geometry via the Borel–Weil Theorem [Bot57] (see [DK00] for an exposition) and moment maps [GS83].”
• ON IDENTIFIABILITY OF NONLINEAR ODE MODELS AND APPLICATIONS IN VIRAL DYNAMICS (2011, unknown): “The interested reader is referred to [36].”