Zobrazeno 1 - 10
of 131
pro vyhledávání: '"Marczinzik, René"'
Auslander and Reiten called a finite dimensional algebra $A$ over a field Cohen-Macaulay if there is an $A$-bimodule $W$ which gives an equivalence between the category of finitely generated $A$-modules of finite projective dimension and the category
Externí odkaz:
http://arxiv.org/abs/2409.05603
Autor:
Cruz, Tiago, Marczinzik, René
We generalise a theorem of Tachikawa about reflexive Auslander-Reiten sequences. We apply this to give a new characterisation of the dominant dimension of gendo-symmetric algebras. We also generalise a formula due to Reiten about the dominant dimensi
Externí odkaz:
http://arxiv.org/abs/2404.02274
We give a combinatorial classification of Nakayama algebras of small homological dimension using the Krattenthaler bijection between Dyck paths and 132-avoiding permutations.
Comment: 14 pages, 13 figures
Comment: 14 pages, 13 figures
Externí odkaz:
http://arxiv.org/abs/2403.11359
Let $KG$ be a group algebra with $G$ a finite group and $K$ a field and $M$ an indecomposable $KG$-module. We pose the question, whether $Ext_{KG}^1(M,M) \neq 0$ implies that $Ext_{KG}^i(M,M) \neq 0$ for all $i \geq 1$. We give a positive answer in s
Externí odkaz:
http://arxiv.org/abs/2310.12748
Autor:
Marczinzik, Rene
Let $A$ be an Iwanaga-Gorenstein ring. Enomoto conjectured that a self-orthogonal $A$-module has finite projective dimension. We prove this conjecture for $A$ having the property that every indecomposable non-projective maximal Cohen-Macaulay module
Externí odkaz:
http://arxiv.org/abs/2303.10433
This work presents results on the finiteness, and on the symmetry properties, of various homological dimensions associated to the Jacobson radical and its higher syzygies, of a semiperfect ring.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/2210.08691
We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their basic properties. We also introduce mixed (pre)cluster tilting modules as a ge
Externí odkaz:
http://arxiv.org/abs/2210.06180
Autor:
Marczinzik, Rene
We show that for a Dynkin quiver $Q$ of type $E_7$ with a specific orientation, the path algebra $KQ$ has no slope function of the form $\mu=\frac{\theta}{\dim}$ that defines a total stability condition. This gives a counterexample to a conjecture of
Externí odkaz:
http://arxiv.org/abs/2205.00947
Autor:
Chavli, Eirini, Marczinzik, Rene
Linear Nakayama algebras over a field $K$ are in natural bijection to Dyck paths and Dyck paths are in natural bijection to 321-avoiding bijections via the Billey-Jockusch-Stanley bijection. Thus to every 321-avoiding permutation $\pi$ we can associa
Externí odkaz:
http://arxiv.org/abs/2204.13764
