Let 1c "be a field and A a finite-dimensional 7c-algebra (associative, with 1). AVe consider representations of A as rings of endomorpliisms of finitedimensional 7c-spaces, and thus JL-modules, and we ask for a classification of such representations. More generally, we may consider the following problem: given an abelian category # and simple ( = irreducible) objects F(l),..., B(n) in #, what a...

A commutative associative algebra A over C with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for A as a vertex algebra and the modules for A as an associative algebra are not well understood. In this paper, I give the classification of finite-dimensional indecomposable untwisted or twisted modules for the polynomial ring in one v...

We provide sufficient conditions for a component of the AuslanderReiten quiver of an Artin algebra to be determined by the composition factors of its indecomposable modules.

In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.

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 show that every entanglement with positive partial transpose may be constructed from an indecomposable positive linear map between matrix algebra.

We consider the continuum scaling limit of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p, p′) as ‘rational’ logarithmic conformal field theories with extendedW symmetry. The representation content is found to consist of 6pp′ − 2p− 2p′ W-indecomposable representations of which 2p+2p′ − 2 are of rank 1, 4pp′ − 2p− 2p′ are of rank 2, while the remaining 2(p− 1)(p′ −...

In this paper, working over Z(p) and using algebra perturbation results from [18], p-minimal homological models of twisted tensor products (TTPs) of Cartan’s elementary complexes are obtained. Moreover, making use of the notion of indecomposability of a TTP, we deduce that a homological model of a indecomposable p-minimal TTP of length ` (` ≥ 2) of exterior and divided power algebras is a tenso...

This dissertation describes an algorithm for constructing the basic algebra Morita equivalent to the principal block of certain group algebras. This algorithm uses the method of condensation as it is described in [Lux97]. Using an intermediate condensation subalgebra allows for the construction of the projective indecomposable modules required to realize the basic algebra. The group algebras we...

In this thesis, we investigate two ways of generalising the preprojective algebra. First, we introduce the multiplicative preprojective algebra, Λ(Q), which is a multiplicative analogue of the deformed preprojective algebra, introduced by Crawley-Boevey and Holland. The special case q = 1 is the undeformed multiplicative preprojective algebra, which is an analogue of the ordinary (undeformed) p...