For indecomposable representations of a finite group G in characteristic p , the theory of vertices and sources introduced by J.A. Green in 1959 [G1] is a fundamental tool in modular representation theory. The vertex and source of an indecomposable module are (up to conjugation) two invariants of the module and only finitely many modules (up to isomorphism) have the same invariants. Thus a natu...

It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category O, or (iii) a module in Category O, or (iv) a module which contains the trivial module as one of its composition factors.

We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category C to be equivalent. This concludes the classification of such module categories.

Let be an artin algebra and denote by mod(() the category of nitely generated-modules. Apart from those we are also interested in-modules which are not nitely generated. These are called large. Recall that the algebra is of innnite representation type provided that mod(() has innnitely many isomorphism classes of indecomposable objects. A theorem of Auslander asserts that there exists a large i...

We give a Decomposition Theorem for a family of Hopf algebras containing the well-know family of Taft Hopf algebras. Therefore, those indecomposable codes over this family of algebras (cf. [4]) is an indecomposable code over the studied case. We use properties of Hopf algebras to show that dual (in the module sense) of an ideal code is again an ideal code.

We give an example of a direct summand of a serial module that does not admit an indecomposable decomposition.

Let W be a finite-dimensional Z/p-module over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W ]Z/p, is called the Noether number of the representation, and is denoted by β(W ). A lower bound for β(W ) is derived, and it is shown that if U is a Z/p submodule of W , then β(U) 6 β(W ). A set of generators, in fact a SAGBI basis, is...

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group SL2, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands. Various other related results are obtained, and numerous examples are computed. Introduction We study the structure of L ⊗ L where L,L are simple modules for the algeb...

We prove that an irreducible quasifinite module over the central extension of the Lie algebra of N × N -matrix differential operators on the circle is either a highest or lowest weight module or else a module of the intermediate series. Furthermore, we give a complete classification of indecomposable uniformly bounded modules.

Two theorems about the vertices of indecomposable Specht modules for the symmetric group, defined over a field of prime characteristic p, are proved: 1. The indecomposable Specht module S has non-trivial cyclic vertex if and only if λ has p-weight 1. 2. If p does not divide n and S(n−r,1 ) is indecomposable then its vertex is a p-Sylow subgroup of Sn−r−1 × Sr. Mathematics Subject Classification...