Let G = SL(2, 5) be the special linear group of 2 × 2-matrices with coefficients in the field with 5 elements. We show that the principal block over a splitting field K of characteristic two of the group algebra KG has a 3-cluster tilting module. This gives the first example of a representation-infinite block of a group algebra having a cluster tilting module and answers a question by Erdmann and Holm.
We present a monomial quiver algebra A having the property that the subcategory Tr(Ω2(mod −A)) is not extension-closed. This answers a question raised by Idun Reiten.
We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups SL2(q) over a large enough field k of positive characteristic ℓ via character-theoretical methods in the cases in which q is odd, ℓ | (q ± 1) when ℓ is odd, and q ≡ ±3 (mod 8) when ℓ = 2.
We present a monomial quiver algebra A having the property that the subcategory Tr(Ω 2 (mod −A)) is not extension-closed. This answers a question raised by Idun Reiten.and the relations are given by I = xy, yz, zx, x 3 . Let S i denote the simple
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