On algebras whose trivial extensions are of finite representation type

1981 ◽  
pp. 364-371 ◽  
Author(s):  
Kunio Yamagata
Keyword(s):  
Representation Type ◽  
Finite Representation ◽  
Finite Representation Type

Auslander algebras Of finite representation type

1987 ◽  
Vol 15 (1-2) ◽  
pp. 377-424 ◽  
Author(s):  
Kiyoshi Igusa ◽  
Maria-Ines Platzeck ◽  
Gordana Todorov ◽  
Dan Zachana
Keyword(s):  
Representation Type ◽  
Finite Representation ◽  
Finite Representation Type

Integer sequences arising from Auslander–Reiten quivers of some hereditary artin algebras

2020 ◽  
pp. 2150051
Author(s):  
Agustín Moreno Cañadas ◽  
Gabriel Bravo Rios ◽  
Hernán Giraldo
Keyword(s):  
Representation Type ◽  
Integer Sequences ◽  
Finite Representation ◽  
Finite Representation Type ◽  
Artin Algebras

Categorification of some integer sequences are obtained by enumerating the number of sections in the Auslander–Reiten quiver of algebras of finite representation type.

Cycles of modules and finite representation type

2016 ◽  
Vol 48 (4) ◽  
pp. 589-600
Author(s):  
Jerzy Białkowski ◽  
Andrzej Skowroński
Keyword(s):  
Representation Type ◽  
Finite Representation ◽  
Finite Representation Type

Group algebras of finite representation type

1983 ◽  
Vol 182 (1) ◽  
pp. 129-148 ◽  
Author(s):  
Hagen Meltzer ◽  
Andrzej Skowroński
Keyword(s):  
Representation Type ◽  
Group Algebras ◽  
Finite Representation ◽  
Finite Representation Type

scholarly journals On Auslander–Reiten sequences for Borel–Schur algebras

2018 ◽  
Vol 17 (02) ◽  
pp. 1850028
Author(s):  
Karin Erdmann ◽  
Ana Paula Santana ◽  
Ivan Yudin
Keyword(s):  
Large Class ◽  
Partial Information ◽  
Representation Type ◽  
Finite Representation ◽  
Schur Algebras ◽  
Finite Representation Type ◽  
Simple Modules

We classify Borel–Schur algebras having finite representation type. We also determine Auslander–Reiten sequences for a large class of simple modules over Borel–Schur algebras. A partial information on the structure of the socles of Borel-Schur algebras is given.

A function on the set of isomorphism classes in the stable category of maximal Cohen-Macaulay modules over a Gorenstein ring: with applications to liaison theory

2017 ◽  
Vol 120 (2) ◽  
pp. 161 ◽  
Author(s):  
Tony J. Puthenpurakal
Keyword(s):  
Local Ring ◽  
Representation Type ◽  
Gorenstein Ring ◽  
Stable Category ◽  
Finite Representation ◽  
Finite Representation Type ◽  
Isomorphism Classes ◽  
Liaison Theory ◽  
Gorenstein Local Ring ◽  
Infinite Set

Let $(A,\mathfrak{m})$ be a Gorenstein local ring of dimension $d \geq 1$. Let $\operatorname{\underline{CM}}(A)$ be the stable category of maximal Cohen-Macauley $A$-modules and let $\operatorname{\underline{ICM}}(A)$ denote the set of isomorphism classes in $\operatorname{\underline{CM}}(A)$. We define a function $\xi \colon \operatorname{\underline{ICM}}(A) \to \mathbb{Z}$ which behaves well with respect to exact triangles in $\operatorname{\underline{CM}}(A)$. We then apply this to (Gorenstein) liaison theory. We prove that if $\dim A \geq 2$ and $A$ is not regular then the even liaison classes of $\{\,\mathfrak{m}^n \mid n\geq 1 \,\}$ is an infinite set. We also prove that if $A$ is Henselian with finite representation type with $A/\mathfrak{m}$ uncountable then for each $m \geq 1$ the set $\mathcal {C}_m = \{\, I \mid I \text { is a codim $2$ CM-ideal with } e_0(A/I) \leq m \,\}$ is contained in finitely many even liaison classes $L_1,\dots ,L_r$ (here $r$ may depend on $m$).

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