#liegroups

#groups #RepresentationTheory #LieGroups

I've worked out that the injectivity radius under the Euclidean metric for the #unitary group U(n) is π and for real and special subgroups O(n), SO(n), and SU(n) is π√2.

This seems like a pretty basic property, but I can't find a single reference that gives the injectivity radii for any of these groups. Anyone know of one?

#DifferentialGeometry #LieGroups #Manifolds

@xameer

Cf. #DifferentialLogic • Discussion 3
• https://inquiryintoinquiry.com/2020/06/17/differential-logic-discussion-3/

Physics once had a #FrameProblem (complexity of dynamic updating) long before AI did but physics learned to reduce complexity through the use of #DifferentialEquations and #GroupSymmetries (combined in #LieGroups). One of the promising features of #MinimalNegationOperators is their relationship to #DifferentialOperators. So I’ve been looking into that. Here’s a link, a bit in medias res, but what I’ve got for now.

I really enjoyed the paper

Oteo & Ros, Why Magnus expansion?, URL: https://doi.org/10.1080/00207160.2021.1938011 (paywall)

and not just because it cites a paper of mine (though it does help!)

It's a historical/personal reflection on the Magnus expansion, a series solution to the differential equation \( x'(t) = A(t) x(t) \) which I describe below the fold. (1/n, n≈7)

#MagnusExpansion #DifferentialEquations #MatrixExponential #QuantumMechanics #LieGroups #NumericalAnalysis #GeometricNumericalIntegration

Hi guys! Is there someone here doing research in #PDE, #LieGroups, #ComplexAnalysis?

#math #mathematics #maths