Projects per year
Abstract
We develop the theory of a category C _{A} which is a generalisation to nonrestricted gmodules of a category famously studied by Andersen, Jantzen and Soergel for restricted gmodules, 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 language  English 

Article number  107033 
Number of pages  52 
Journal  Journal of Pure and Applied Algebra 
Volume  226 
Issue number  8 
Early online date  26 Jan 2022 
DOIs  
Publication status  Published  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.
Keywords
 Modular Lie algebra
 Baby Verma module
 Induction
 Projective cover
ASJC Scopus subject areas
 Algebra and Number Theory
Fingerprint
Dive into the research topics of 'On graded representations of modular Lie algebras over commutative algebras'. Together they form a unique fingerprint.Projects
 1 Finished

Representation theory of modular Lie algebras and superalgebras
Engineering & Physical Science Research Council
1/07/18 → 31/12/22
Project: Research Councils