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Mathematics
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Advances in Algebraic Structures: Representation Theory and Lie Groups
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Advances in Algebraic Structures: Representation Theory and Lie Groups

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 24 November 2025 | Viewed by 1202

Special Issue Editor

Dr. Guy Biyogmam

E-Mail Website
Guest Editor
Department of Mathematics, Georgia College & State University, Milledgeville, GA, USA
Interests: lie algebras; leibniz algebras and their representations; leibniz algebra cohomology

Special Issue Information

Dear Colleagues,

Understanding the structure of Lie groups using representation theory has become an important topic of research in modern mathematics with a wide variety of applications in many fields, ranging from differential geometry, algebraic geometry, or Riemannian geometry to mechanics, robotics, or gauge theory in physics. Consequently, authors publishing papers in these areas may be better served by a platform that tracks recent development and applications of Lie groups and their representations.

This Special Issue aims to collect reviews and original research papers on various topics concerning the recent progress in the theory of Lie groups, Lie algebras, and their representation. This includes research on other disciplines that involves information of and relationship with Lie groups.

Dr. Guy Biyogmam
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • algebraic structures
  • algebraic groups
  • lie groups
  • lie algebras
  • representation theory
  • root systems
  • coxeter groups
  • characteristic classes
  • flag varieties
  • quantum groups
  • holonomy
  • variational methods

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

10 pages, 243 KiB  
Article
Relative Vertex-Source-Pairs of Modules of and Idempotent Morita Equivalences of Rings
by Morton E. Harris
Mathematics 2025, 13(15), 2327; https://doi.org/10.3390/math13152327 - 22 Jul 2025
Viewed by 24
Abstract
Here all rings have identities. Let R be a ring and let R-mod denote the additive category of left finitely generated R-modules. Note that if R is a noetherian ring, then R-mod is an abelian category and every R-module [...] Read more.
Here all rings have identities. Let R be a ring and let R-mod denote the additive category of left finitely generated R-modules. Note that if R is a noetherian ring, then R-mod is an abelian category and every R-module is a finite direct sum of indecomposable R-modules. Finite Group Modular Representation Theory concerns the study of left finitely generated OG-modules where G is a finite group and O is a complete discrete valuation ring with O/J(O) a field of prime characteristic p. Thus OG is a noetherian O-algebra. The Green Theory in this area yields for each isomorphism type of finitely generated indecomposable (and hence for each isomorphism type of finitely generated simple OG-module) a theory of vertices and sources invariants. The vertices are derived from the set of p-subgroups of G. As suggested by the above, in Basic Definition and Main Results for Rings Section, let Σ be a fixed subset of subrings of the ring R and we develop a theory of Σ-vertices and sources for finitely generated R-modules. We conclude Basic Definition and Main Results for Rings Section with examples and show that our results are compatible with a ring isomorphic to R. For Idempotent Morita Equivalence and Virtual Vertex-Source Pairs of Modules of a Ring Section, let e be an idempotent of R such that R=ReR. Set B=eRe so that B is a subring of R with identity e. Then, the functions eR⊗R∗:R−mod→B−mod and Re⊗B∗:B−mod→R−mod form a Morita Categorical Equivalence. We show, in this Section, that such a categorical equivalence is compatible with our vertex-source theory. In Two Applications with Idemptent Morita Equivalence Section, we show such compatibility for source algebras in Finite Group Block Theory and for naturally Morita Equivalent Algebras. Full article
(This article belongs to the Special Issue Advances in Algebraic Structures: Representation Theory and Lie Groups)
8 pages, 218 KiB  
Article
A Zassenhaus Lemma for Digroups
by Guy Roger Biyogmam
Mathematics 2024, 12(19), 2972; https://doi.org/10.3390/math12192972 - 25 Sep 2024
Viewed by 686
Abstract
In this paper, we construct a quotient structure on digroups. This construction yields a new functor from the category of digroups to the category of groups. We obtain a modular property for digroups and use it to prove an analogue of the Zassenhaus [...] Read more.
In this paper, we construct a quotient structure on digroups. This construction yields a new functor from the category of digroups to the category of groups. We obtain a modular property for digroups and use it to prove an analogue of the Zassenhaus lemma in this framework. Full article
(This article belongs to the Special Issue Advances in Algebraic Structures: Representation Theory and Lie Groups)
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