The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach

On Indecomposable Modules over the Virasoro Algebra

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.

Modules over the 4-dimensional Sklyanin Algebra

egalement que l'alg ebre de Sklyanin peut ^ etre d eenie a l'aide des bilin eaires s'annulant sur une certaine sous-vari et e de P 3 P 3 : ABSTRACT. This paper studies point modules and line modules over the algebra deened by E.K. Sklyanin in 17]. It was proved in 21] that the point modules are in bijection with the points of an elliptic curve E in P 3 together with 4 other points. Here it is p...

The q-tetrahedron algebra and its finite dimensional irreducible modules

Recently B. Hartwig and the second author found a presentation for the three-point sl2 loop algebra via generators and relations. To obtain this presentation they defined an algebra ⊠ by generators and relations, and displayed an isomorphism from ⊠ to the three-point sl2 loop algebra. We introduce a quantum analog of ⊠ which we call ⊠q. We define ⊠q via generators and relations. We show how ⊠q ...

Algorithms for computer algebra

Regularity of Modules over a Koszul Algebra

We prove that every module over a commutative homogeneous Koszul algebra has regularity bounded by its regularity over a polynomial ring of which the Koszul algebra is a homomorphic image. From this we derive a result conjectured by George Kempf to the effect that a suffkiently high truncation of any module over a homogeneous Koszul algebra has a linear free resolution. ‘E’ 1992 Academic Press....