All Questions
11 questions with no upvoted or accepted answers
7
votes
0
answers
275
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Split epimorphism of modules - does the finite case imply the infinite case?
Let $k$ be a field, $A$ a finite dimensional $k$-algebra, $X$ a finite dimensional indecomposable (left) $A$-module and $M$ an infinite dimensional (left) $A$-module. Suppose further we have an ...
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6
votes
0
answers
178
views
Ext for commutative Gorenstein algebras
Let $A$ be a finite dimensional commutative Gorenstein $K$-algebra over a field $K$.
Question 1: Is there an easy example of $A$-modules $M$ and $N$ such that $\mathrm{Ext}_A^1(M,N)=0$ but $\mathrm{...
- 26.5k
5
votes
0
answers
132
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On a reference for computing global spectrum of $A_n$-curve singularities, by H.Dao and E.Faber
This question is about chasing down a reference in a paper relating to non-commutative crepant resolutions and Cohen-Macaulay representation theory.
Allow me to first give a minor introduction.
Let $(...
- 51
4
votes
0
answers
114
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Classification of 2-periodic triangulated categories
Let $T$ be an algebraic triangulated (k-linear over a field, Hom-finite, idempotent-complete) category. Call $T$ 2-periodic if $\Omega^2(X) \cong X$ for all $X \in T$.
Question 1: Is there a ...
- 26.5k
4
votes
0
answers
196
views
Quillen–Suslin theorem in a more general context
Let $A$ be a finite dimensional local Frobenius algebra that is Koszul.
Question: Is it true for the Koszul dual of $A$ that every finitely generated projective module is free? If not, is there a ...
- 26.5k
4
votes
0
answers
76
views
Minimal rank of a permutation resolution of a $G$-lattice
Let $G$ be a finite group.
By a $G$-lattice I mean a finitely generated free abelian group $L$ with an action of $G$.
One says that $L$ is a permutation lattice if $L$ has a $\mathbb{Z}$-basis ...
- 14.2k
3
votes
0
answers
175
views
Geometric interpretation of homological quantities in Artinian local Gorenstein algebras
By corollary 3.5. of http://www.ams.org/journals/tran/2012-364-09/S0002-9947-2012-05430-4/S0002-9947-2012-05430-4.pdf the classification of local artinian Gorenstein algebras (all algebras here are ...
- 26.5k
2
votes
0
answers
196
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Commutative local rings which satisfy Krull-Remak-Schmidt
Question 1: Can the class of local (always noetherian and commutative) rings be classified for which the Krull-Remak-Schmidt theorem (KRS) holds for finitely generated modules? They contain for ...
- 26.5k
2
votes
0
answers
135
views
Ext over a certain commutative algebra
Let $A$ be the algebra $K[x,y]/(x^2,y^2,xy,yx)$. Then $A$ is a 3-dimensional commutative algebra and $Ext^i(M,A) \neq 0$ for any indecomposable non-projective module $M$ for some $i>0$. Namely: $...
- 26.5k
1
vote
0
answers
106
views
Uniqueness of indecomposable decomposition (Krull–Schmidt) for finitely generated modules over commutative Noetherian standard graded rings
Let $R_0=\mathbb C$ and $R=\bigoplus_{i\geq 0} R_i$ be a commutative Noetherian graded ring such that the grading is standard, i.e., $R=R_0[R_1]$. Let $M$ be a finitely generated $R$-module. Evidently,...
- 412
1
vote
0
answers
60
views
$Ext^i(D(R),R)$ for a certain commutative algebra
Let $k$ be a field which is not algebraic over a finite field and $a \in k$ an element of infinite multiplicative order.
Let $R=k[V,X,Y,Z]/I$ with $I=<V^2,Z^2,XY,VX+aXZ,VY+YZ,VX+Y^2,VY-X^2>.$
...
- 26.5k