In this paper, we shall study nonperiodic connected components of the stable Auslander Reiten quiver of a reduced enveloping algebra u(L, /) associated to a restricted Lie algebra (L, [ p]). According to earlier results (cf. [13,15]) the tree classes of these AR-components are either Euclidean diagrams, or the infinite Dynkin diagrams A , D , A . In the context of finite groups, K. Erdmann has recently shown that the latter two trees cannot occur for wild blocks (cf. [12]). As demonstrated in [13,19], a similar result holds for the restricted enveloping algebra u(L) :=u(L, 0) in case the underlying Lie algebra L is nilpotent and of characteristic p 3. Here neither tame blocks nor components of tree class A or D exist. For p=2 the restricted enveloping algebra of the 2-unipotent Heisenberg algebra possesses components of tree class A . Presently, no Lie algebra admitting components of tree class D is known, and recent work [20] suggests that such components will be rather exceptional.
In default of a general block theory for enveloping algebras one is led to either employ geometric techniques (cf. [20]) or to focus on those cases, where the block structure of u(L, /) is governed by well-understood ``linkage principles'' (cf. [13,18,19]). The former are most effective for Lie algebras of algebraic groups, while the latter for instance play a ro^le in the AR-theory of supersolvable Lie algebras.
Our paper can roughly be divided into two parts. The purpose of Sections 1 through 3 is to furnish basic properties of components of infinite Dynkin type. By using a modification of a recognition criterion due to Erdmann [12], in Section 2 we provide general results pertaining to the aforementioned components. Components of tree class A are discussed in