In this paper we describe all gradings by a finite abelian group G on the following Lie algebras over an algebraically closed field F of characteristic p = 2: sl n (F) (n not divisible by p), so n (F) (n ≥ 5, n = 8) and sp n (F) (n ≥ 6, n even).
For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple Lie algebras of types An (n ≥ 1), Bn (n ≥ 2), Cn (n ≥ 3) and Dn (n > 4), in terms of numerical and group-theoretical invariants. The ground field is assumed to be algebraically closed of characteristic different from 2.
Our aim is to construct new examples of totally ordered and *-ordered noncommutative integral domains. We will discuss the following classes of rings: enveloping algebras U (L), group rings kG and smash products U (L)# ϕ kG. All of them are examples of Hopf algebras. Characterizations of orderability for enveloping algebras and group rings and of… (More)
Known classification results allow us to find the number of fine gradings on matrix algebras and on classical simple Lie algebras over an algebraically closed field (assuming that characteristic is not 2 in the Lie case). The computation is easy for matrix algebras and especially for simple Lie algebras of Series B, but involves counting orbits of certain… (More)