Commutative Restricted Lie Algebras1

Commutative Restricted Lie Algebras1

Examples of such algebras are subspaces of associative algebras of characteristic p^O which are closed under the Lie multiplication [ab] =ab — ba and under pih powers. Then one may take a[pl =ap. It is known that every restricted Lie algebra is isomorphic to one of this type. For this reason we may simplify our notation in the sequel and write a" for alp]. We call the mapping a—>ap the p-operat...

A Note on the Representations of Nilpotent Lie Algebras1

On the Restricted Lie Algebra Structure for the Witt Lie Algebra in Finite Characteristic

The Lie algebra W = DerA is called the Witt algebra. It consists of “vector fields” f∂, f ∈ A. In particular, dimF W = dimF A = p. As any Lie algebra of derivations of a commutative algebra over F, W has a canonical structure of a restricted Lie algebra. Recall that a restricted Lie algebra is a Lie algebra over F with an additional unary (in general, non-linear) operation g 7→ g satisfying the...

On generalized reduced representations of restricted Lie superalgebras in prime characteristic

Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. These quotient superalgebras are called the generalized reduced enveloping ...

SUBREGULAR REPRESENTATIONS OF sln AND SIMPLE SINGULARITIES OF TYPE An−1 IAIN GORDON AND DMITRIY RUMYNIN

Alexander Premet has stated the following problem: what is a relation between subregular nilpotent representations of a classical semisimple restricted Lie algebra and non-commutative deformations of the corresponding singularities? We solve this problem for type A.