Lie Groups, Lie Algebras, and Representations

By B. Hall. 2003

2,082 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

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Citations in the corpus

Deep Learning on Lie Groups for Skeleton-Based Action Recognition (2016, background): “parts, and the number of rotation matrices is 2C2 M (C 2 is the combination formula). The set of n nnrotation matrices in R forms the special orthogonal group SO nwhich is actually a matrix Lie group [22,9,16]. Accordingly, each motion sequence of a moving skeleton is represented with a curve on the”
Discriminative virtual views for cross-view action recognition (2012, background): “Further assuming equal prior probabilities for the two classes, we approximate the objective in (3) by I(x̂; c) .”
SE(3) diffusion model with application to protein backbone generation (2023, positive): “Using that SU(2) is connected we have that for any U ∈ SU(2) there exists X ∈ su(2) such that U = exp[X] and using that π ◦ exp = exp ◦ρ, (Hall, 2015, Theorem 3.7), we get that π(SU(2))(W ) ⊂ W and therefore W = V .”
Explorations in Homeomorphic Variational Auto-Encoding (2018, methodology): “Alternatively, we propose a method based on the representation theory of groups (Hall, 2003).”
Contact-aided invariant extended Kalman filtering for robot state estimation (2019, methodology): “Definition 2 (The adjoint map (Hall, 2015: 63)).”
Discovering Structural Regularity in 3D Geometry (2008, neutral): “According to the general theory of matrix groups [Hall 2003], for every choice of d, d̄, δ there is a unique one-parameter subgroup T (τ) = exp(τ ·D) such that (3) is valid.”
Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups (2013, neutral): “In the case of matrix Lie groups, we have the following formula [33] Ad( M ) .”
Human Action Recognition by Representing 3D Skeletons as Points in a Lie Group (2014, methodology): “We refer the readers to [4] for a general introduction to Lie groups and [11] for further details on SE(3) and rigid body kinematics.”
iSAM2: Incremental smoothing and mapping using the Bayes tree (2012, methodology): “For optimization over 3D orientations, the ⊕ operator is implemented using exponential maps based on the theory of Lie groups (Hall, 2000), with the ﬁrst visual SLAM application of SAM shown in Del-laert and Kaess (2006) based on Euler angles.”
Lie groups, Lie algebras, and their representations (2015, neutral): “Other sources that treat the material in these notes are [1], [2], [4], [9] and [7].”