Indecomposable Modules for Finite Groups

The strong no loop conjecture for special biserial algebras

“…First of all, since their representations are completely understood, they form naturally a testing class for various well-known conjectures in the representation theory of algebras. Secondly, these algebras play an important role in the modular representation theory of finite groups; see [7], tracing back to the classification of the indecomposable HarishChandra modules of the Lorentz group by Gelfand and Ponomarev; see [4].…”

The representation-finite symmetric algebras with liftable simple modules

“…In [8] G. J. Janusz showed that a p-block algebra Λ of a finite group G of finite representation type over a splitting field F with characteristic p > 0 is uniserial if and only if every simple Λ-module M can uniquely be lifted to a simpleΛ ⊗ R Smodule, where R is a complete discrete rank one valuation ring R with maximal ideal πR, residue class field F = R/πR, and quotient field S with characteristic zero, and whereΛ is an RG-block such that Λ ∼ =Λ ⊗ R F . If Λ has at least two non-isomorphic simple modules, then using standard results of the theory of blocks with cyclic defect groups [5], p. 302, and J.…”

A classification of symmetric algebras of strictly canonical type

“…In the representation theory of blocks of group algebras, a prominent role is played by the Brauer tree algebras. Namely, by the deep theorem due to Dade, Janusz and Kupisch (see [1], [13], [18], [19], [20]), every block of finite representation type of a group algebra is Morita equivalent to a Brauer tree algebra. More-over, by results of Gabriel and Riedtmann [15] and Rickard [30], the Brauer tree algebras are exactly the symmetric algebras which are stably equivalent and derived equivalent to the symmetric Nakayama algebras.…”