Prépublications

• Monoidal invariance of the cohomological dimension of Hopf algebras: the finite case. hal-05508721, ArXiv:2602.12731. To appear in Arkiv för Mathematik.
• (With Thi Hoa Emilie Nguyen) Cohomological dimension of braided Hopf algebras. hal-04746722, arXiv:2410.16768. To appear in Documenta Mathematica.
  

Publications

56. (With Agustín García Iglesias) Hopf-Galois objects over bicrossed product Hopf algebras and twisting maps. New York Journal of Mathematics 32 (2026), 771-807. Link.
55. Bialgebra cohomology and exact sequences, Comptes Rendus - Mathématique 362 (2024), 1475-1483. Link.
54. Twisted separability for adjoint functors, Theory and Applications of Categories 41 (2024), 150-167. Link.
53. On the monoidal invariance of the cohomological dimension of Hopf algebras, Comptes Rendus - Mathématique 360 (2022), 561-582. Link
52. (With Maeva Paradis) Some isomorphism results for graded twistings of function algebras on finite groups, Annales de la Faculté des Sciences de Toulouse - Mathématiques 31 (2022), no. 2, 501-544. Link
51. (With Agustín García Iglesias) Hopf-Galois structures on ambiskew polynomial rings, Journal of Noncommutative Geometry 15 (2021), no. 4, 1409-1431.
50. Cohomological dimensions of universal cosovereign Hopf algebras, Publicacions Matemàtiques 62 (2018), no. 2, 301-330. Link
49. (With David Kyed and Sven Raum) Higher L2-Betti numbers for universal quantum groups, Canadian Mathematical Bulletin 61 (2018), no. 2, 235-245.
48. (With Sergey Neshveyev and Makoto Yamashita) Graded twisting of comodule algebras and module categories, Journal of Noncommutative Geometry 12 (2018), no. 1, 331-368.
47. (With Uwe Franz and Malte Gerhold) Homological properties of quantum permutation algebras , New York Journal of Mathematics 23 (2017), 1671-1695. Link
46. (With Teodor Banica) Complex analogues of the half-classical geometry, Münster Journal of Mathematics 10(2017), 457-483.
45. (With Teodor Banica) Matrix models for noncommutative algebraic manifolds, Journal of the London Mathematical Society 95 (2017, 519-540.
44. (With Sergey Neshveyev and Makoto Yamashita) Graded twisting of categories and quantum groups by group actions, Annales de l'Institut Fourier 66 (2016), 2299-2338. Link.
43. Half-liberated real spheres and their subspaces, Colloquium Mathematicum 144 (2016), 273-287.
42. Gerstenhaber-Schack and Hochschild cohomologies of Hopf algebras, Documenta Mathematica 21 (2016), 955-986. Link
41. The group of bi-Galois objects over the coordinate algebra of the Frobenius-Lusztig kernel of SL(2), Glasgow Mathematical Journal 58, 727-738, 2016.
40. (With Simon Riche) Hopf algebras having a dense big cell, Transactions of the American Mathematical Society 368, 515-538, 2016. Link .
39. Quotients and Hopf images of a smash coproduct, Tsukuba Journal of Mathematics 39(2), 285-310, 2015. Link
38. (With Teodor Banica) Random walk questions for linear quantum groups, International Mathematics Research Notices 2015(24), 13406-13436, 2015.
37. (With Robert Yuncken) Quantum subgroups of the compact quantum group SU_-1(3), Bulletin of the London Mathematical Society 46, 315-328, 2014.
36. Hopf-Galois objects and cogroupoids, Revista de la Unión Matemática Argentina 55(2), 11-69, 2014. Link
35. (With Michel Dubois-Violette) The quantum group of a preregular multilinear form, Letters in Mathematical Physics 113, 455-468, 2013.
34. Hochschild homology of Hopf algebras and free Yetter-Drinfeld resolutions of the counit, Compositio Mathematica 149, 658-678, 2013.
33. (With Michel Dubois-Violette) Half-commutative orthogonal Hopf algebras, Pacific Journal of Mathematics 263-1, 13-28, 2013.
32. (With Teodor Banica, Benoît Collins and Stephen Curran) A maximality result for orthogonal quantum groups, Communications in Algebra 41, 656-665, 2013.
31. (With Teodor Banica et Sonia Natale) Finite quantum groups and quantum permutation groups, Advances in Mathematics 229, 3320-3338, 2012. Link
30. (With Teodor Banica and Stephen Curran) Quantum automorphisms of twisted group algebras and free hypergeometric laws, Proceedings of the American Mathematical Society 139, 3961-3971, 2011. Link
29. (With Sonia Natale) Hopf algebra deformations of binary polyhedral groups, Transformation Groups 16, 339-374, 2011.
28. (With Nicolás Andruskiewitsch) Examples of inner linear Hopf algebras, Revista de la Unión Matemática Argentina 51, 7-18, 2010. Link
27. (With Teodor Banica) Hopf images and inner faithful representations, Glasgow Mathematical Journal 52, 677-703, 2010.
26. (With Christian Kassel) The lazy homology of a Hopf algebra, Journal of Algebra 323, 2556-2590, 2010. Link
25. (With Teodor Banica and Jean-Marc Schlenker ) Representations of quantum permutation algebras, Journal of Functional Analysis 257, 2864-2910, 2009. Link
24. (With Teodor Banica) Quantum groups acting on 4 points, Journal für die Reine und Angewandte Mathematik (Crelle's Journal) 626, 75-114, 2009.
23. Algebraic quantum permutation groups, Asian-European Journal of Mathematics 1, 1-13, 2008.
22. (With Teodor Banica and Benoît Collins) The hyperoctahedral quantum group, Journal of the Ramanujan Mathematical Society 22, 345-384, 2007.
21. (With Teodor Banica and Benoît Collins) Quantum permutation groups: a survey, Banach Center Publications 78, 13-34, 2007.
20. (With Teodor Banica and Gaëtan Chenevier), Graphs having no quantum symmetry, Annales de l'Institut Fourier 57, 955-971, 2007. Link
19. (With Teodor Banica) Quantum automorphism groups of vertex-transitive graphs of order ≤ 11, Journal of Algebraic Combinatorics 26, 83-105, 2007.
18. (With Teodor Banica) Free Product Formulae for Quantum Permutation Groups, Journal de l'Institut de Mathématiques de Jussieu 6, 381-414, 2007.
17. Corepresentation Theory of Universal Cosovereign Hopf Algebras, Journal of the London Mathematical Society 75, 83-98, 2007.
16. (With An De Rijdt and Stefaan Vaes) Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups, Communications in Mathematical Physics 262, 703-728, 2006.
15. (With Giovanna Carnovale) Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras, Journal of Pure and Applied Algebra 204(3), 627-665, 2006. Link
14. Galois and biGalois objects over monomial non-semisimple Hopf Algebras, Journal of Algebra and its Applications 5(5), 653-680, 2006.
13. Free quantum analogues of the first fundamental theorems of invariant theory, Proceedings of the Edinburgh Mathematical Society 47, 297-303, 2004.
12. Free wreath product by the quantum permutation group, Algebras and Representation Theory 7(4), 343-362, 2004.
11. N-complexes et algèbres de Hopf, Comptes Rendus de l'Académie des Sciences 337, 441-444, 2003. Link
10. Hopf-Galois systems, Journal of Algebra 264, 565-581, 2003. Link
9. The representation category of the quantum group of a non-degenerate bilinear form, Communications in Algebra 31 (10), 4831-4851, 2003.
8. (With Ross Street) Militaru's $D$-equation in monoidal categories , Applied Categorical Structures 11 (4), 337-357, 2003.
7. Quantum automorphism groups of finite graphs, Proceedings of the American Mathematical Society 131(3), 665-673, 2003. Link
6. Cosemisimple Hopf algebras with antipode of arbitrary finite order, New-York Journal of Mathematics 8, 235-240, 2002. Link
5. Cosovereign Hopf algebras, Journal of Pure and Applied Algebra 157(2-3), 121-133, 2001. Link
4. Quelques nouvelles déformations du groupe symétrique., Comptes Rendus de l'Académie des Sciences 330 (9), 761-764, 2000. Link
3. Galois reconstruction of finite quantum groups, Journal of Algebra 230, 683-693, 2000. Link
2. Mesure de Haar sur une algèbre de Hopf et groupes quantiques réels, Communications in Algebra 26 (5), 1633-1649, 1998.
1. Trivialisations dans les catégories tannakiennes, Cahiers de topologie et géométrie différentielle catégoriques 39 (4), 243-270, 1998.

• Faithful flatness of Hopf algebras over coideal subalgebras with a bimodule conditional expectation. hal-03936040, arXiv:2301.05480.
• Cohomological dimension of Hopf algebras. Lecture notes for a mini-course given at Córdoba (2017).
• Homological invariants of discrete quantum groups. Lecture notes for a mini-course given at Seoul (2017).
• Introduction aux groupes quantiques : cours de M2 en 2008-2009.
• Systèmes de Hopf-Galois : exemples et applications aux représentations des groupes quantiques. Mémoire de synthèse pour l'habilitation à diriger des recherches (2004).
• Some classical spaces realized as mutational spaces (2003).
• Galois extension for a compact quantum group (1997/1999).
• Trivialisations dans les catégories tannakiennes. Version longue de 1996.

Exposés

• About the monoidal invariance of cohomological dimension of Hopf algebras, Quantum Groups Seminar, Online (2021).
• Cohomological dimensions of Hopf algebras, Greifswald (2016)
• Finite quantum groups and quantum permutation groups, Almeria (2011)