All Questions
Tagged with ra.rings-and-algebras koszul-algebras
13 questions
3
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Non-commutative Gorenstein Koszul algebras
I was wondering if there exists a characterization of finite-dimensional Gorenstein Koszul algebras in terms of their Koszul dual?
- 63.9k
3
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100
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Pairing on a Koszul dual pair
Let $A$ be a graded quadratic algebra over a field $k$, and suppose that it admits the Koszul dual $A^!$. I want to know if there is a natural pairing $A\otimes A^!\to k$ or something similar to this. ...
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$M^2=0$ defines a Koszul algebra ? What if $M$ is Manin's endomorphism's of Koszul $A$ ? (Here $M^2=\sum_k M_{ik}M_{kj}$ - resembles $d^2=0$).)
Consider a matrix $M$ which elements $M_{ij}$ are generators of some algebra $K$,
impose new relations: $M^2=0$ and get a new algebra $K_{2}$.
Question 1: Is it true that $K_2$ is Koszul algebra when ...
- 24.9k
3
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Filtering a pre-Koszul algebra to get a homogeneous associated graded algebra
In Priddy's paper "Koszul resolutions", on p. 42 he defines an algebra $A$ to be pre-Koszul if it can be written as a quotient of a free algebra $F = F\langle x_i \rangle$ with generators $\{...
- 4,254
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Does Manin's construction of non-commutative endomorphism algebra $\mathrm{End}(A)$ produce Koszul algebra, if $A$ is Koszul?
$\newcommand{\dual}{\mathrm{dual}}\DeclareMathOperator\End{End}\DeclareMathOperator\Fun{Fun}\DeclareMathOperator\Spec{Spec}\DeclareMathOperator\GL{GL}$Around 1986–7 Yu.Manin proposed natural and ...
- 16.9k
13
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1
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Is algebra: ac=ca, bd = db , ad - da = cb - bc ("Manin matrix algebra") - a Koszul algebra?
Question: Consider quadratic algebra with four generators $a,b,c,d,d$ and three relations $ac=ca,bd = db, ad-da = cb - bc$ . Is it a Koszul algebra ? (i.e. Koszul complex is resolution of ground field ...
- 24.9k
2
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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 ...
0
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2
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205
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Quotients of Koszul algebras
Let $A$ be a noncommutative Koszul algebra (see here for a definition of Koszul) and let $c \in A$ be a central element. Will the quotient of $A$ by the ideal generated by $c$ again be Koszul. If not ...
- 44.7k
3
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What is an example of a Frobenius algebra that is not Koszul?
What is an example of a Frobenius algebra that is not Koszul? Are there reasonable requirements for a Frobenius to be Koszul?
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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 $i$. ...
- 3,686
14
votes
2
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689
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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 \...
- 16.9k
25
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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 ...
- 1,028
2
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1
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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)
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