Showing papers on "Cartan matrix published in 1969"

Graded lie algebras of finite characteristic

Abstract: An invariant description is given of finite-dimensional algebras of Cartan type and, with certain restrictions, they are identified with abstract graded Lie algebras defined over algebraically closed fields of characteristic p > 7.

Euclidean Lie Algebras

Abstract: Our aim in this paper is to study a certain class of Lie algebras which arose naturally in (4). In (4), we showed that beginning with an indecomposable symmetrizable generalized Cartan matrix (A ij) and a field Φ of characteristic zero, we could construct a Lie algebra E((A ij)) over Φ patterned on the finite-dimensional split simple Lie algebras. We were able to show that E((A ij)) is simple providing that (A ij) does not fall in the list given in (4, Table). We did not prove the converse, however. The diagrams of the table of (4) appear in Table 2. Call the matrices that they represent Euclidean matrices and their corresponding algebras Euclidean Lie algebras. Our first objective is to show that Euclidean Lie algebras are not simple.