Representation Type and Stable Auslander-Reiten Components for Reduced Enveloping Algebras of Cartan Type

Abstract

On Problem 8 of Benkart and Feldvoss: the representation type of the blocks of u_chi(g) for g a restricted simple Lie algebra of Cartan type, and the shapes of the stable Auslander-Reiten components. For terminal blocks with p >= 7 every nonperiodic stable component is one of ZA_infinity, ZA_infinity^infinity and ZD_infinity; the p = 7 terminal simple component is ZA_infinity, and complexity three forces the same for p >= 11. For r = p - 4 and p >= 7 the Euclidean stable components are excluded block-wide. On the rank-three canonical row strip the ambient-semisimple packet universe is reduced to four points.