arXiv subjects

Jacopo Zanchettin

Publications and source records attributed to Jacopo Zanchettin.

3 recordsLinked to original sources

arXiv2025

The Chern-Weil homomorphism for deformed Hopf-Galois extensions

In this article, we study the Chern-Weil theory for Hopf-Galois extensions originally introduced by Hajac and Maszczyk in the context of coalgebra extensions. We show that the cyclic homology Chern-Weil homomorphism defines natural transformations between Hopf-Galois extensions with a strong connection (principal comodule algebras) and cyclic homology, thereby generalizing the concept of characteristic classes to the noncommutative setting. In the second part, we study the effect of $2$-cocycle deformations of Hopf-Galois extensions on the aforementioned homomorphism. We consider the $2$-cocycle coming from the structure Hopf algebra of the extension, an external symmetry, and finally the combined case.

math.QA↗

arXiv2024

Hopf algebroids and twists for quantum projective spaces

We study the relationship between antipodes on a Hopf algebroid $\mathcal{H}$ in the sense of Böhm-Szlachanyi and the group of twists that lies inside the associated convolution algebra. We specialize to the case of a faithfully flat $H$-Hopf-Galois extensions $B\subseteq A$ and related Ehresmann-Schauenburg bialgebroid. In particular, we find that the twists are in one-to-one correspondence with $H$-comodule algebra automorphism of $A$. We work out in detail the $U(1)$-extension ${\mathcal O}(\mathbb{C}P^{n-1}_q)\subseteq {\mathcal O}(S^{2n-1}_q)$ on the quantum projective space and show how to get an antipode on the bialgebroid out of the $K$-theory of the base algebra ${\mathcal O}(\mathbb{C}P^{n-1}_q)$.

math.QA↗

arXiv2021

Twisted Spectral Triples without the First-Order Condition

We extend twisted inner fluctuations to twisted spectral triples that do not meet the twisted first-order condition, following what has been done in [6] for the non-twisted case. We find a similar non-linear term in the fluctuation, and work out the twisted version of the semi-group of inner perturbations.

math-ph↗