Generalized Kac-Moody Lie algebras can be defined starting from any matrix in terms of generators and relations. It is well known that Kac-Moody Lie superalgebras can have several Cartan matrices. We define an abstract notion of a root groupoid generalizing the Weyl group. It leads us to the notion of root algebra which, roughly speaking, respects the symmetries determined by a root groupoid. In the classical case, this approach allows us to define Serre's relations from Chevalley relations. Sometimes there are several root algebras defined by a given root groupoid. The description of all root algebras is an open question. One application of this approach is the classification of Kac-Moody superalgebras of finite growth.

This is a joint work with M. Gorelik and V. Hinich.