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Mathematics
Special Issues
Lie Theory and Its Applications
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Lie Theory and Its Applications

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

Deadline for manuscript submissions: closed (31 July 2019) | Viewed by 2713

Special Issue Editor

Prof. Dr. Hadi Salmasian

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave., Ottawa, ON K1N 6N5, Canada
Interests: representation theory of lie groups; lie algebras and lie superalgebras

Special Issue Information

Dear Colleagues,

Lie theory is one of the most active domains of mathematical research, with a long history and a wide range of applications both within and outside mathematics. Its inception dates back to the work of Sophus Lie, who used continuous symmetries in studying differential equations. Nowadays, Lie theory interacts with many branches of pure and applied mathematics. In particular, the representation theory of Lie theoretic objects is a vast source of interesting ideas that interconnect abstract algebra, topology, combinatorics, and category theory.

The goal of this Special Issue is to publish articles on the latest advancements in Lie theory and its applications. Submitted manuscripts should meet high standards of exposition and mathematical precision.

Prof. Dr. Hadi Salmasian
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

  • Lie Groups
  • Lie Algebras
  • Lie Superalgebras
  • Representation Theory
  • Noncommutative harmonic analysis
  • Algebraic combinatorics
  • Category theory

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Published Papers (1 paper)

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Research

5 pages, 208 KiB  
Article
Some Results on the Cohomology of Line Bundles on the Three Dimensional Flag Variety
by Muhammad Fazeel Anwar
Mathematics 2019, 7(3), 295; https://doi.org/10.3390/math7030295 - 22 Mar 2019
Viewed by 2203
Abstract
Let k be an algebraically closed field of prime characteristic and let G be a semisimple, simply connected, linear algebraic group. It is an open problem to find the cohomology of line bundles on the flag variety G / B , where B [...] Read more.
Let k be an algebraically closed field of prime characteristic and let G be a semisimple, simply connected, linear algebraic group. It is an open problem to find the cohomology of line bundles on the flag variety G / B , where B is a Borel subgroup of G. In this paper we consider this problem in the case of G = S L 3 ( k ) and compute the cohomology for the case when ⟨ λ , α ∨ ⟩ = − p n a − 1 , ( 1 ≤ a ≤ p , n > 0 ) or ⟨ λ , α ∨ ⟩ = − p n − r , ( r ≥ 2 , n ≥ 0 ) . We also give the corresponding results for the two dimensional modules N α ( λ ) . These results will help us understand the representations of S L 3 ( k ) in the given cases. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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