We develop the theory of a category CA 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 Uχ 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 develop here certain important modules ZA,χ(λ), QIA,χ(λ) and QA,χ(λ) in CA which generalise familiar objects when A=𝕂, and we prove some key structural results regarding them.
|Journal||Journal of Pure and Applied Algebra|
|Publication status||Accepted/In press - 5 Jan 2022|
- Modular Lie algebra
- Baby Verma module
- Projective cover
ASJC Scopus subject areas
- Algebra and Number Theory