On graded representations of modular Lie algebras over commutative algebras

Research output: Contribution to journalArticlepeer-review

5 Downloads (Pure)


We develop the theory of a category C A which is a generalisation to non-restricted g-modules of a category famously studied by Andersen, Jantzen and Soergel for restricted g-modules, where g is the Lie algebra of a reductive group G over an algebraically closed field K of characteristic p>0. Its objects are certain graded bimodules. On the left, they are graded modules over an algebra U χ associated to g and to χ∈g in standard Levi form. On the right, they are modules over a commutative Noetherian S(h)-algebra A, where h is the Lie algebra of a maximal torus of G. We define here certain important modules Z A,χ(λ), Q A,χ I(λ) and Q A,χ(λ) in C A which generalise familiar objects when A=K, and we prove some key structural results regarding them.

Original languageEnglish
Article number107033
Number of pages52
JournalJournal of Pure and Applied Algebra
Issue number8
Early online date26 Jan 2022
Publication statusPublished - Aug 2022

Bibliographical note

Funding Information:
The author was supported during this research by EPSRC grant EP/R018952/1 . He would like to thank Simon Goodwin for many useful discussions about this subject and for his opinions on an earlier version of this paper, as well as the referee for their comments. The author has no competing interests to declare.


  • Modular Lie algebra
  • Baby Verma module
  • Induction
  • Projective cover

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'On graded representations of modular Lie algebras over commutative algebras'. Together they form a unique fingerprint.

Cite this