Lie Algebras and Groups
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: closed (15 October 2019) | Viewed by 1808
Special Issue Editor
Interests: markov type lie algebras and monoids; entropy and information theory; generalized lie algebras; riemannian geometry reformulated as a generalized lie algebra; mathematical network theory; lie algebras as representing observable operators for measurements; representation theory; nonlinear differential equations
Special Issue Information
Dear Colleagues,
Sophus Lie’s formulation of continuous transformations utilized the concept of “infinitesimal generators” that formed a new mathematical structure, a “Lie algebra”, whose exponential map generated continuous transformations, or “Lie groups”. A Lie algebra is a linear vector space with an antisymmetric product obeying the Jacobi identity and denoting another member of the algebra as a linear combination (structure constant), a basic element of algebra. They formed the foundational symmetries of translations and Lorentz transformations in the Poincare symmetry algebra. The Heisenberg Lie algebra provided the basis of quantum theory with differential operators rather than matrices, producing the Fourier transform method. Lie algebras were soon used to represent approximate symmetries, then “spectrum generating” algebras, algebras of observables, and the “standard model”. We are learning to reframe earlier mathematics as representations of extended Lie algebras in new fields: diffusion, entropy, information theory, and the equations of general relativity are now revealing new patterns.
Dr. Joseph Johnson
Guest Editor
Manuscript Submission Information
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Keywords
- Lie algebras
- Lie groups
- Fourier and harmonic analysis
- Information theory
- Entropy
- Differential equations
- Non-linear systems
- Markov transformations
- Approximate symmetry
- Topological spaces