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3 votes
0 answers
97 views

What algebras generate polynomial count varieties as their representations spaces ? Is it preserved by the Koszul duality, Manin's endomorphisms?

Consider for example commutative polynomial algebra $C[x,y]: xy=yx$, look on $F_p$-matrices satisfying that relation - the number over $F_p$ will be given by polynomial in $p$ (classical result due to ...
6 votes
1 answer
231 views

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 ...
13 votes
1 answer
598 views

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 ...
7 votes
0 answers
433 views

What is the endomorphism cooperad?

In Loday and Vallette's book on algebraic operads, they use the "Endomorphism cooperad $End^c_{s\mathbb{K}}$", where $s\mathbb{K}$ is the base field, shifted into (homological) degree one. This is an ...