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Trisections of module categories

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de la Peña J., Reiten I.

Colloquium Mathematicum

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2007

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tom 107

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nr 2

191-219

EN

Let A be a finite-dimensional algebra over a field k. We discuss the existence of trisections (mod₊ A,mod₀ A,mod₋ A) of the category of finitely generated modules mod A satisfying exactness, standardness, separation and adjustment conditions. Many important classes of algebras admit trisections. We describe a construction of algebras admitting a trisection of their module categories and, in special cases, we describe the structure of the components of the Auslander-Reiten quiver lying in mod₀ A.

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Graded modules and their completions

100%

Auslander M., Reiten I.

Banach Center Publications

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1990

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tom 26

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nr 1

181-192

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Additive functions for quivers with relations

100%

Lenzing H., Reiten I.

Colloquium Mathematicum

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1999

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tom 82

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nr 1

85-103

EN

Additive functions for quivers with relations extend the classical concept of additive functions for graphs. It is shown that the concept, recently introduced by T. Hübner in a special context, can be defined for different homological levels. The existence of such functions for level 2 resp. ∞ relates to a nonzero radical of the Tits resp. Euler form. We derive the existence of nonnegative additive functions from a family of stable tubes which stay tubes in the derived category, we investigate when this situation does appear and we study the restrictions imposed by the existence of a positive additive function.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Banach Center Publications

3 Reiten I.

1 Auslander M.

1 Lenzing H.

1 de la Peña J.

1 2007

1 1999

1 1990

Trisections of module categories

Graded modules and their completions

Additive functions for quivers with relations