Simple Lie algebras and Lie algebras of maximal class (Q1337753)

Given a field \(k\) of arbitrary positive characteristic, we construct infinite-dimensional graded Lie algebras over \(k\) which are non-soluble and have maximal class. A key to the construction is the use of finite- dimensional simple Lie algebras which admit a cyclic grading and a non- singular derivation moving the 1-dimensional homogeneous components cyclically.