Galois actions and blocks of tame infinitesimal group schemes

Abstract

Abstract. Given an infinitesimal group G, that is defined over an algebraically closed field of characteristic p ≥ 3, we determine the block structure of the algebra of measures H(G) in case its principal block B 0 (G) is tame and the height of the factor group G/M(G) of G by its multiplicative center M(G) is at least two. Our results yield a complete description of the stable Auslander-Reiten quiver of H(G) along with a criterion for the domesticity of H(G).

The Krull-Gabriel Dimension of Cycle-Finite Artin Algebras

“…In particular, for n = 2, we have the following special case of Schröer's conjecture: for an algebra A of infinite representation, KG(A) = 2 if and only if m≥1 (rad ∞ A ) m = 0. It has been confirmed for the following classes of algebras: the tilted algebras of Euclidean type [22,23], the algebras stably equivalent to tame hereditary algebras [23], the algebras with directing indecomposable projective modules [65], the enveloping algebras of restricted Lie algebras [19] (more generally, the infinitesimal group schemes [20]) in odd characteristic, the strongly simply connected algebras [61,69], the 1-domestic string algebras [44,45,51], and recently the tame generalized multicoil algebras [31].…”

Derived equivalence classification of Brauer graph algebras

“…Brauer graph algebras first emerged in modular representation theory in form of blocks with cyclic [Dad66] or dihedral defect group [Don79]. Thereafter, these algebras appeared in other classification results such as in the classification of self-injective cellular algebras of polynomial growth [AKMW17], tame blocks of Hecke algebras [Ari18,Ari17], symmetric 2-Calabi-Yau-tilted algebras of finite representation type [Lad16], and blocks of tame infinitesimal group schemes [FS07]. Recently, Brauer graph algebras also appeared in connection with dessins d'enfants [MS20].…”

On the structure of tame graded basic Hopf algebras II

“…by Farnsteiner and his cooperators recently [20] [18][21] [17] [19]. The representation theory of such cocommutative Hopf algebras was also studied in [15] [16].…”