# Questions tagged [koszul-algebras]

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

13
questions

**4**

votes

**0**answers

81 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/...

**1**

vote

**1**answer

71 views

### Augmented algebras over semisimple ring

Let $A$ be a non-negatively graded algebra such that $A_0 = k$. We say that $A$ is Koszul if $k$ has a projective resolution by projective modules such that the i-th piece is generated in degree $i$. ...

**1**

vote

**1**answer

238 views

### Complete intersection subvariety of projective variety

I am not able to find any literature which studies complete intersection subvarieties of a projective variety, all good references consider CI in projective space.
My guess is, a subvariety X of ...

**4**

votes

**0**answers

168 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 ...

**3**

votes

**1**answer

404 views

### What bigrading is used in this spectral sequence?

I am reading this paper of Positselski and Vishik, in particular the main theorem: the cohomology algebra of a conilpotent algebra (i.e. the cohomology of its cobar construction) is Koszul if it ...

**2**

votes

**1**answer

91 views

### Description of Koszul dual of Sklyanin algebras

It is well-known that Sklyanin algebras are Koszul, but, is it known an explicit description of the dual algebra Ext_A(k,k)? (I mean in terms of generators and relations)

**5**

votes

**1**answer

286 views

### Non-commutative regular sequences and non-commutative Koszul complex

I'm trying to understand the non-commutative Koszul complex, as can be found in Anick's nice paper "Non-Commutative Graded Algebras and Their Hilbert Series", J. of Algebra 78, (1982) and I'm stuck at ...

**3**

votes

**1**answer

177 views

### Is Koszulity equivalent to the Lusztig character formula holding?

Let $\pi$ denote a saturated set of weights. Let $S_q(\pi)$ denote the associated generalised $q$-Schur algebra. I was wondering if the following claim is true:
Claim: The algebra $S_q(\pi)$ is ...

**6**

votes

**1**answer

233 views

### Is the (super-)symmetric power of the exterior algebra free?

Let $V$ be a vector space over $k$ of dimension $m$. (I'm only interested in the case $k=\mathbb{Q}$.) Let $R:=\Lambda^*V$ be the exterior algebra. It carries the structure of a supercommutative ring: ...

**1**

vote

**1**answer

169 views

### Koszul algebras deformations

Do we know the maximal class of Koszul algebras for which any deformation is Koszul?

**14**

votes

**2**answers

543 views

### Koszulness of the cohomology ring of moduli of stable genus zero curves

Let $n \geq 3$. The ring $H^\bullet(\overline{M}_{0,n},\mathbf Q)$ was determined by Sean Keel. It is generated by the cohomology classes of boundary divisors $D_{A,B}$ corresponding to partitions $A \...

**20**

votes

**2**answers

2k views

### Koszul duality between Weyl and Clifford algebras?

Koszul duality
Given a finite-dimensional $k$-vector space $V$ (I am happy taking $k = \mathbb{C}$ anywhere in the following if it makes a difference) and a subspace $R \subseteq V \otimes V$, we can ...

**12**

votes

**2**answers

1k views

### Clifford PBW theorem for quadratic form

Update: now with a question 2 which is much more elementary (and should be well-known!).
Let $k$ be a commutative ring with $1$. Let $L$ be a $k$-module, and $g:L\to k$ be a quadratic form, i. e., a ...