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This page contains some information about the Research Unit of University of Turin within the national research project:
Structures for Quivers, Algebras and Representations (SQUARE).
Principal Investigator: Lidia Angeleri (Univ. Verona)
supported by the European Union - NextGenerationEU under NRRP, Mission 4 Component
2 CUP D53D23005960006 - Call PRIN 2022 No. 104 of February 2, 2022 of Italian Ministry of University and Research; Project 2022S97PMY
Brief description of the objectives of the Turin unit within the project
Brief description of the objectives of the Turin unit within the project
We consider bialgebras and use functorial techniques to address questions such as existence of integrals or Hopf structures. Finally, we study categorical properties of some class of Hopf algebras.
Goals of the Turin unit
Goals of the Turin unit
Construct and investigate a space of left integrals on an arbitrary bialgebra without requiring the existence of an antipode. Understand how being Frobenius for functors that are central to the study of modules over bialgebra-like objects, reflects on the algebraic properties of the latter ones. Understend how far a suitable class of Hopf algebra is from being semi-abelian.
Unit participants of Univ. Turin
Unit participants of Univ. Turin
Alessandro Ardizzoni (Associate Professor, Unit coordinator)
Alan Cigoli (Associate Professor)
Davide Ferri (Ph.D. student)
Andrea Sciandra (Ph.D. student)
Zhenbang Zuo (Ph.D. student)
Unit participant recruited under the project PRIN2022
Unit participant recruited under the project PRIN2022
Lucrezia Bottegoni (Post-Doc. Title: Frobenius functors, Separable functors and semi-abelian categories)
Unit participants from other universities
Unit participants from other universities
Claudia Menini (Full Professor, Univ. Ferrara)
Unit collaborators from other universities
Unit collaborators from other universities
Marino Gran (UCLouvain)
Paolo Saracco (Univ. Sevilla)
Fabio Renda (Univ. Ferrara)
Events organized
Events organized
"Symposium on Quivers, Algebras and Representation Theory" (SQUARE), Hotel Montana, Trento (Italy), June 23-27, 2025. (Homepage)
“Hopf Algebras and Monoidal Categories”, University of Ferrara (Italy), September 3-6, 2024. (Homepage)
"4th ItaCa Workshop", University of Turin (Italy), December 18-19, 2023. (Homepage)
Publications
Publications
D. Ferri, A. Sciandra, Matched pairs and Yetter-Drinfeld braces, Canad. J. Math. (2025) (doi.org/10.4153/S0008414X25000239)
A. Sciandra, Yetter-Drinfeld post-Hopf algebras and Yetter-Drinfeld relative Rota-Baxter operators, J. Noncommut. Geom. (2025) Online First. (doi.org/10.4171/jncg/621)
Preprints
Preprints
A. Sciandra, Commutators and crossed modules of color Hopf algebras, preprint. (arXiv:2312.00156)
D. Ferri, On dynamical skew braces and skew bracoids. preprint. (arXiv:2410.10717).
M. Gran, A. Sciandra, Hopf braces and semi-abelian categories, preprint. (arXiv:2411.19238)
L. Bottegoni, F. Renda, A. Sciandra, Infinitesimal R-matrices for some families of Hopf algebras, preprint. (arXiv:2412.02350)
A. Ardizzoni, C. Menini, P. Saracco, On the Hopf envelope of finite-dimensional bialgebras, preprint. (arxiv:2504.05821)
D. Ferri, Reflections and Drinfeld twists for set-theoretic Yang-Baxter maps, preprint. (arxiv:2504.21678)
A. Ardizzoni, A. Sciandra, The binary product in the 2-category of triangular bialgebras and twisted morphisms, preprint. (arxiv:2506.16469)
M. Gran, A. Sciandra, Hopf formulae for cocommutative Hopf algebras, preprint. (arXiv:2509.09992)
D. Ferri, Split Lemma and First Isomorphism Theorem for groupoids, preprint. (arXiv:2509.13973)
A. Ardizzoni, C.. Menini, Paolo Saracco, Integrals for Bialgebras, preprint. (arXiv:2509.14823)
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