# Varieties of elementary subalgebras of maximal dimension for modular Lie algebras

@article{Pevtsova2015VarietiesOE, title={Varieties of elementary subalgebras of maximal dimension for modular Lie algebras}, author={J. Pevtsova and Jim Stark}, journal={arXiv: Representation Theory}, year={2015} }

Motivated by questions in modular representation theory, Carlson, Friedlander, and the first author introduced the varieties E(r, g) of r-dimensional abelian p-nilpotent subalgebras of a p-restricted Lie algebra g. In this paper, we identify the varieties E(r, g) for a reductive restricted Lie algebra g and r the maximal dimension of an abelian p-nilpotent subalgebra of g.

## 9 Citations

### Varieties of elementary subalgebras of submaximal rank in type A

- Mathematics
- 2017

Let G be a connected simple algebraic group over an algebraically closed field k of characteristic p > 0, and g := Lie(G). We additionally assume that G is standard and is of type An. Motivated by…

### Commuting Varieties and Cohomological Complexity

- Mathematics
- 2021

. In this paper we determine, for all r suﬃciently large, the irreducible component(s) of maximal dimension of the variety of commuting r -tuples of nilpotent elements of gl n . Our main result is…

### Integration questions in separably good characteristics

- Mathematics
- 2021

Let G be a reductive group over an algebraically closed field k of separably good characteristic p > 0 for G. Under these assumptions a Springer isomorphism φ : Nred(g)→ Vred(G) always exists,…

### Analogues of Morozov Theorem in characteristic p>0

- Mathematics
- 2021

Let k be an algebraically closed ﬁeld of characteristic p > 0 and let G be a reductive k - group. In this article we prove an analogue of Morozov’s Theorem when p is separably good for G and under…

### A modular analogue of Morozov's theorem on maximal subalgebras of simple Lie algebras

- Mathematics
- 2015

### Commuting varieties and cohomological complexity theory

- MathematicsJournal of the London Mathematical Society
- 2022

In this paper we determine, for all r$r$ sufficiently large, the irreducible component(s) of maximal dimension of the variety of commuting r$r$ ‐tuples of nilpotent elements of gln$\mathfrak {gl}_n$…

### Varieties of a class of elementary subalgebras

- MathematicsAIMS Mathematics
- 2021

Let $ G $ be a connected standard simple algebraic group of type $ C $ or $ D $ over an algebraically closed field $ \Bbbk $ of positive characteristic $ p > 0 $, and $ \mathfrak{g}: =…

### Varieties of elementary abelian Lie algebras and degrees of modules

- MathematicsRepresentation Theory of the American Mathematical Society
- 2021

<p>Let <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis German g comma left-bracket p right-bracket right-parenthesis">…

## References

SHOWING 1-10 OF 40 REFERENCES

### Abelian ideals in a Borel subalgebra of a complex simple Lie algebra

- Mathematics
- 2004

Let $\mathfrak{g}$ be a complex simple Lie algebra and $\mathfrak{b}$ a fixed Borel subalgebra of $\mathfrak{g}$. We describe the abelian ideals in $\mathfrak{b}$ in a uniform way, that is,…

### The Spectrum of an Equivariant Cohomology Ring: II

- Mathematics
- 1971

Let G be a compact Lie group (e.g., a finite group) and let HG= H*(BG, Z/pZ) be its mod p cohomology ring. One knows this ring is finitely generated, hence upon dividing out by the ideal of nilpotent…

### Vector Bundles Associated to Lie Algebras

- Mathematics
- 2014

We introduce and investigate a functorial construction which associates coherent sheaves to finite dimensional (restricted) representations of a restricted Lie algebra $\mathfrak g$. These are…

### Simple groups of Lie type

- Mathematics
- 1972

Partial table of contents: The Classical Simple Groups. Weyl Groups. Simple Lie Algebras. The Chevalley Groups. Unipotent Subgroups. The Diagonal and Monomial Subgroups. The Bruhat Decomposition.…

### ON WEIGHT MODULES OF ALGEBRAS OF TWISTED DIFFERENTIAL OPERATORS ON THE PROJECTIVE SPACE

- Mathematics
- 2013

We classify blocks of categories of weight and generalized weight modules of algebras of twisted differential operators on ℙn. Necessary and sufficient conditions for these blocks to be tame and…

### The Book of Involutions

- Mathematics
- 1998

This monograph yields a comprehensive exposition of the theory of central simple algebras with involution, in relation with linear algebraic groups. It aims to provide the algebra-theoretic…