Questions tagged [koszul-algebras]

Questions about Koszul algebras as defined by Priddy (1970) and generalizations.

7 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
7 votes
0 answers
197 views

On the center of Koszul Lie algebras

The short question is the following: If a positively graded Lie algebra $\mathfrak g$ over a field $F$ is Koszul, is the center of $\mathfrak g$ concentrated in degree $1$? Let us be more precise. A ...
Simone Blumer's user avatar
5 votes
0 answers
213 views

Koszul duality between QLS algebras and cdg algebras

A Quadratic-Linear-Constant (QLC) algebra $U$ is an algebra which can be written as $T(V)/P$ where $T(V) = \bigoplus_{n \in \mathbb{N}} V^{\otimes n}$ is the tensor algebra and $P \subseteq k \oplus ...
Chris Kuo's user avatar
  • 525
4 votes
0 answers
94 views

Koszul algebras among finite dimensional commutative algebras

Given a local commutative artinian algebra $A$ of the form $K[x_1,...,x_n]/I$ with quadratic ideal $I$ and $K$ a field. Question 1: Is there a computer algebra system that can check whether such an ...
Mare's user avatar
  • 25.8k
4 votes
0 answers
180 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 ...
Mare's user avatar
  • 25.8k
4 votes
0 answers
113 views

Perfect modules for the Beilinson algebra

The Beilinson algebra $A=A_n$ is a finite dimensional quiver algebra that is derived equivalent to the category of coherent sheaves of $\mathcal{P}^n$. See for example https://link.springer.com/...
Mare's user avatar
  • 25.8k
2 votes
0 answers
104 views

Filtrations and Koszul algebras

I was looking at this question and asked my self the following: Let $A$ be graded algebra, which is also an $\mathbb{N}_0$-filtered algebra. If its associated graded algebra $\mathrm{gr}(A)$ is ...
Didier de Montblazon's user avatar
1 vote
0 answers
98 views

When is a Koszul algebra derived equivalent to its dual

Let $A$ be a finite dimensional Koszul algebra of finite global dimension. Question: When is $A$ derived equivalent to its Koszul dual algebra? I wonder whether there is an exact condition to ...
Mare's user avatar
  • 25.8k