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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Varieties of elementary abelian Lie algebras and degrees of modules
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by Hao Chang and Rolf Farnsteiner
Represent. Theory 25 (2021), 90-141
Published electronically: February 11, 2021


Let $(\mathfrak {g},[p])$ be a restricted Lie algebra over an algebraically closed field $k$ of characteristic $p\!\ge \!3$. Motivated by the behavior of geometric invariants of the so-called $(\mathfrak {g},[p])$-modules of constant $j$-rank ($j \in \{1,\ldots ,p\!-\!1\}$), we study the projective variety $\mathbb {E}(2,\mathfrak {g})$ of two-dimensional elementary abelian subalgebras. If $p\!\ge \!5$, then the topological space $\mathbb {E}(2,\mathfrak {g}/C(\mathfrak {g}))$, associated to the factor algebra of $\mathfrak {g}$ by its center $C(\mathfrak {g})$, is shown to be connected. We give applications concerning categories of $(\mathfrak {g},[p])$-modules of constant $j$-rank and certain invariants, called $j$-degrees.
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Bibliographic Information
  • Hao Chang
  • Affiliation: School of Mathematics and Statistics, Central China Normal University, 430079 Wuhan, People’s Republic of China
  • ORCID: 0000-0002-0137-0586
  • Email:
  • Rolf Farnsteiner
  • Affiliation: Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany
  • MR Author ID: 194225
  • Email:
  • Received by editor(s): April 22, 2020
  • Received by editor(s) in revised form: December 5, 2020
  • Published electronically: February 11, 2021
  • Additional Notes: The first author was partially supported by the National Natural Science Foundation of China (No. 11801204).

  • Dedicated: Dedicated to Jens Carsten Jantzen on the occasion of his 70th birthday
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 90-141
  • MSC (2020): Primary 17B50, 16G10
  • DOI:
  • MathSciNet review: 4214336