On Auslander-Reiten quivers of enveloping algebras of restricted Lie algebras

Let (L, [p]) be a finite dimensional restricted Lie algebra over an algebra ically closed field F of characteristic p greater than or equal to 3, chi i s an element of L* a linear form. In this article we study the Auslander-Re iten quivers of certain blocks of the reduced enveloping algebra u(L, chi). In particular, it is shown that the enveloping algebras of supersolvable L ie algebras do not possess AR -components of Euclidean type.