This paper investigates a class of infinite-dimensional Lie algebras over a field of characteristic 0 which are called here Lie algebras of generalized Block type, and which generalize a class of Lie algebras originally defined by Richard Block. Under certain natural restrictions, this class of Lie algebras is shown to break into five subclasses. One of these subclasses contains all generalized Cartan type K Lie algebras and some Lie algebras of generalized Cartan type H, and a second one is the class of Lie algebras type L, which were previously defined and studied elsewhere by the authors. The other three types are hybrids of the first two types, and are new.
Osborn, J. Marshall and Zhao, Kaiming, "Infinite-Dimensional Lie Algebras of Generalized Block Type" (1999). Mathematics Faculty Publications. 52.