On construction of differential $\mathbb Z$-graded varieties

Abstract: Given a commutative unital algebra $\mathcal O$, a proper ideal $I$ in $\mathcal O$, and a positively graded differential variety over $\mathcal{O}/I,$ we provide a $\mathbb Z$-graded extension, whose negative part is an arborescent Koszul-Tate resolution of $\mathcal{O}/I.$ This extension is obtained through an algorithm exploiting the explicit homotopy retract data of the arborescent Koszul-Tate resolution, so that the number of homological computations in the construction is significantly reduced. For a positively graded differential variety over $\mathcal O$ that preserves the ideal $I$, the extension admits a manifest description in terms of decorated trees and computed data.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar