Group Gradings on Simple Lie Algebras in Positive Characteristic
نویسندگان
چکیده
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: sln(F ) (n not divisible by p), son(F ) (n ≥ 5, n = 8) and spn(F ) (n ≥ 6, n even).
منابع مشابه
Group Gradings on Simple Lie Algebras of Type a in Positive Characteristic
In this paper we consider gradings by a finite abelian group G on the Lie algebra sln(F ) over an algebraically closed field F of characteristic different from 2 and not dividing n.
متن کاملFine Gradings on Simple Classical Lie Algebras
The fine abelian group gradings on the simple classical Lie algebras (including D4) over algebraically closed fields of characteristic 0 are determined up to equivalence. This is achieved by assigning certain invariant to such gradings that involve central graded division algebras and suitable sesquilinear forms on free modules over them.
متن کاملGraded Simple Lie Algebras and Graded Simple Representations
For any finitely generated abelian group Q, we reduce the problem of classification of Q-graded simple Lie algebras over an algebraically closed field of “good” characteristic to the problem of classification of gradings on simple Lie algebras. In particular, we obtain the full classification of finite-dimensional Q-graded simple Lie algebras over any algebraically closed field of characteristi...
متن کاملCounting Fine Gradings on Matrix Algebras and on Classical Simple Lie Algebras
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 finite groups in the case of Series A, ...
متن کامل2 00 5 Group Gradings on Simple Lie Algebras of Type “ A ”
In this paper we describe all group gradings by a finite abelian group G of any Lie algebra L of the type " A " over algebraically closed field F of characteristic zero.
متن کامل