The Green Ring of a Restricted Enveloping Algebra in Characteristic 2

Let k be an algebraically closed field of characteristic 2 and let fsl(2) fsl ( 2 ) be the unique, up to isomorphism, 3-dimensional simple Lie algebra over k . Denote by m m the minimal 2-envelope of fsl(2) fsl ( 2 ) and by u(m) u ( m ) its corresponding restricted enveloping algebra. The non-isomorphic finite-dimensional indecomposable u(m) u ( m ) -modules were classified in [1]. In this paper, the Green ring (or representation ring) for u(m) u ( m ) is calculated. Also, the semisimplification of the representation category of u(m) u ( m ) is determined.