Cartan desompositions and BGG-resolutions.
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Categorical methods in graded ring theory.
Angel del Río (1992)
Publicacions Matemàtiques
Let G be a group, R a G-graded ring and X a right G-set. We study functors between categories of modules graded by G-sets, continuing the work of [M]. As an application we obtain generalizations of Cohen-Montgomery Duality Theorems by categorical methods. Then we study when some functors introduced in [M] (which generalize some functors ocurring in [D1], [D2] and [NRV]) are separable. Finally we obtain an application to the study of the weak dimension of a group graded ring.
Central extensions of three dimensional Artin-Schelter regular algebras.
Lieven Le Bruyn, M. Van den Bergh (1996)
Mathematische Zeitschrift
Character Modules
D.J. Fieldhouse (1971)
Commentarii mathematici Helvetici
Cohomological Properties of Modules with Secondary Representations.
Leif Melkersson (1995)
Mathematica Scandinavica
Combinatorial topology and the global dimension of algebras arising in combinatorics
Stuart Margolis, Franco Saliola, Benjamin Steinberg (2015)
Journal of the European Mathematical Society
In a highly influential paper, Bidigare, Hanlon and Rockmore showed that a number of popular Markov chains are random walks on the faces of a hyperplane arrangement. Their analysis of these Markov chains took advantage of the monoid structure on the set of faces. This theory was later extended by Brown to a larger class of monoids called left regular bands. In both cases, the representation theory of these monoids played a prominent role. In particular, it was used to compute the spectrum of the...
Complexity and periodicity
Petter Andreas Bergh (2006)
Colloquium Mathematicae
Let M be a finitely generated module over an Artin algebra. By considering the lengths of the modules in the minimal projective resolution of M, we obtain the Betti sequence of M. This sequence must be bounded if M is eventually periodic, but the converse fails to hold in general. We give conditions under which it holds, using techniques from Hochschild cohomology. We also provide a result which under certain conditions guarantees the existence of periodic modules. Finally, we study the case when...
Construction of Auslander-Gorenstein local rings as Frobenius extensions
Mitsuo Hoshino, Noritsugu Kameyama, Hirotaka Koga (2015)
Colloquium Mathematicae
Starting from an arbitrary ring R we provide a systematic construction of ℤ/nℤ-graded rings A which are Frobenius extensions of R, and show that under mild assumptions, A is an Auslander-Gorenstein local ring if and only if so is R.
Correction to: Homological Dimension and Stationary Sets. Math. Z. 180, 1-9 (1982).
Paul C. Eklof (1983)
Mathematische Zeitschrift
Correction to: Maximal orders of global dimension and Krull dimension two.
M. Artin (1987)
Inventiones mathematicae
Cycle-finite algebras with almost all indecomposable modules of projective or injective dimension at most one
Adam Skowyrski (2013)
Colloquium Mathematicae
We describe the structure of artin algebras for which all cycles of indecomposable modules are finite and almost all indecomposable modules have projective or injective dimension at most one.
Currently displaying 1 – 11 of 11
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