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Symmetry
Special Issues
Lie Algebras and Groups
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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 2417

Special Issue Editor

Dr. Joseph Johnson

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Guest Editor
Distinguished Professor Emeritus, Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208, USA
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

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Lie algebras
  • Lie groups
  • Fourier and harmonic analysis
  • Information theory
  • Entropy
  • Differential equations
  • Non-linear systems
  • Markov transformations
  • Approximate symmetry
  • Topological spaces

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Published Papers (1 paper)

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Research

7 pages, 259 KiB  
Article
On Finite Quasi-Core-p p-Groups
by Jiao Wang and Xiuyun Guo
Symmetry 2019, 11(9), 1147; https://doi.org/10.3390/sym11091147 - 10 Sep 2019
Cited by 1 | Viewed by 1818
Abstract
Given a positive integer n, a finite group G is called quasi-core-n if ⟨ x ⟩ / ⟨ x ⟩ G has order at most n for any element x in G, where ⟨ x ⟩ G is the normal [...] Read more.
Given a positive integer n, a finite group G is called quasi-core-n if ⟨ x ⟩ / ⟨ x ⟩ G has order at most n for any element x in G, where ⟨ x ⟩ G is the normal core of ⟨ x ⟩ in G. In this paper, we investigate the structure of finite quasi-core-p p-groups. We prove that if the nilpotency class of a quasi-core-p p-group is p + m , then the exponent of its commutator subgroup cannot exceed p m + 1 , where p is an odd prime and m is non-negative. If p = 3 , we prove that every quasi-core-3 3-group has nilpotency class at most 5 and its commutator subgroup is of exponent at most 9. We also show that the Frattini subgroup of a quasi-core-2 2-group is abelian. Full article
(This article belongs to the Special Issue Lie Algebras and Groups)
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