We classify the Harish-Chandra modules over the higher rank Virasoro and super-Virasoro algebras: It is proved that a Harish-Chandra module, i.e., an irreducible weight module with finite weight multiplicities, over a higher rank Virasoro or super-Virasoro algebra is a module of the intermediate series. As an application, it is also proved that an indecomposable weight module with finite weight...

In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive modules, if there is a nonfree cyclic totally reflexive module.

Generic modules have been introduced by Crawley-Boevey in order to provide a better understanding of nite dimensional algebras of tame representation type. In fact he has shown that the generic modules correspond to the one-parameter families of indecomposable nite dimensional modules over a tame algebra 5]. The Second Brauer-Thrall Conjecture provides another reason to study generic modules be...

We give a new proof of the fact that any finite quadratic module can be decomposed into indecomposable ones. For module, we construct lattice, and positive definite both which are least rank, whose discriminant is given one. The resulting lattices by their Gram matrices explicitly.

Let (R,m) be a local ring (commutative and Noetherian). If R is complete (or, more generally, Henselian), one has the Krull-Schmidt uniqueness theorem for direct sums of indecomposable finitely generated R-modules. By passing to the m-adic completion b R, we can get a measure of how badly the Krull-Schmidt theorem can fail for a more general local ring. We assign to each finitely generated R-mo...

We describe the representation theory of finitely generated indecomposable modules over artin algebras which do not lie on cycles involving homomorphisms from infinite Jacobson radical module category.

We study certain filtrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warfield. To indicate the consequences of our analysis, suppose that g is a complex classical simple Lie superalgebra and that E is an indecomposable injective g-module with nonzero (and so necessarily s...

k field, algebraically closed G finite group Definitions (1) A representation of G over k of degree n is a homomorphism of groups ρ : G→GLn(k), or equivalently, a kG-module structure for an n-dimensional k vector space M , where kG is the group algebra. (2) A representation M is irreducible if it is a simple kG-module, and indecomposable if M 6= N1 ⊕ N2 for any non-trivial submodules N1, N2. No...

We study certain ltrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warreld. To indicate the consequences of our analysis, suppose that g is a complex classical simple Lie superalgebra and that E is an indecomposable injective g-module with nonzero (and so necessarily simp...

The concept of an algebraic module originated with Alperin [1]. It can be thought of as an attempt to distinguish those modules whose tensor powers are ‘nice’ from those whose tensor powers are ‘uncontrollable’. Define a module to be algebraic if it satisfies a polynomial with integer coefficients in the Green ring. This is equivalent to the statement that for a module M there is a finite list ...