(main)

research interests

I am interested in Hopf algebras and Nichols algebras. I study their classification and their representation theory.
In this framework, my favorite algebras are the Fomin-Kirrilov algebras \(FK_n\) and the generalized small quantum groups.
Two paradigmatic problems are surrounding my works and involve these algebras. First, it is not known whether or not
the Fomin-Kirillov algebras are finite or infinite dimensional for \(n \geq 6\). Second, most of my recent works are about
the representation theory of generalized small quantum groups. In the examples, I have observed that the Hilbert series
of their simple modules are palindromic and I would like to verify if this property holds true in general.

See also my profiles in arXiv, Google Scholar, MathSciNet, ResearchGate and zbMATH.

collaborators

publications & preprints (and slides, posters and other stuff)

			Linkage principle for small quantum groups
			Koszul duality for Coxeter groups Ann. Represent. Theory 1 (2024), no. 3, 335-374. with S. Riche.
			The Green ring of a family of copointed Hopf algebras Rev. Un. Mat. Argentina 68 (2025), no. 1, 23-48.
			Simple modules of small quantum groups at dihedral groups Doc. Math. 29 (2024), no. 1, 1-38. with G. García.
			On the Hopf algebra structure of the Lusztig quantum divided power algebras Annales Mathématiques Blaise Pascal 27 (2020), no. 2, 131-157. with N. Andruskiewitsch and I. Angiono
			On Hopf algebras with triangular decomposition Contemp. Math. 728 (2019), 181-199.
			Mixed perverse sheaves on flag varieties of Coxeter groups Canad. J. Math. 72 (2020), no. 1, 1-55. with P. Achar and S. Riche.
			On the representation theory of the Drinfeld double of the Fomin-Kirillov algebra \(\mathcal{FK}_3\) Algebr. Represent. Theory 22 (2019), no. 6, 1399-1426. with B. Pogorelsky.
		GAP file	Copointed Hopf algebras over \(\mathbb{S}_4\) J. Pure Appl. Algebra 222 (2018), no. 9, 2784-2809. with A. García Iglesias.
			On projective modules over finite quantum groups Transf. Groups 24 (2019), no. 1, 279-299.
			Explicit coproduct formula for quantum group of the type \(G_2\) J. Algebra 500 (2018) 103-116. with V. Kharchenko.
			Verma and simple modules for quantum groups at non-abelian groups Adv. Math. 301 (2016) 423-457. with B. Pogorelsky.
			The cohomology ring of the 12-dimensional Fomin-Kirillov algebra Adv. Math. 291 (2016) 584-620. with D. Stefan.
			Acerca de las álgebras de Fomin-Kirillov Actas Congr. "Dr. Antonio A. R. Monteiro'' (2015), Univ. Nac. del Sur, Bahía Blanca, 43-54.
			Representations of copointed Hopf algebras arising from the tetrahedron rack Ann. Univ. Ferrara Sez. VII Sci. Mat. 60 (2014), no. 2, 407-427. with B. Pogorelsky.
			Finite-dimensional pointed or copointed Hopf algebras over affine racks J. Algebra 397 (2014) 379-406. with A. García Iglesias.
			Lifting via cocycle deformation J. Pure Appl. Algebra 218 (2014), no. 4, 684-703. with N. Andruskiewitsch , I. Angiono , A. García Iglesias and A. Masuoka.
			From Hopf algebras to tensor categories Conformal Field Theories and Tensor Categories, Yi-Zhu Huang et al. editors, Mathematical Lectures from Peking University, Springer. with N. Andruskiewitsch , I. Angiono , A. García Iglesias and B. Torrecillas.
			On a family of Hopf algebras of dimension 72 Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 3, 415-443. with N. Andruskiewitsch.
			Finite dimensional Hopf algebras over the dual group algebra of the symmetric group in three letters Comm. Algebra 39 (2011), no. 12, 4507-4517. with N. Andruskiewitsch.
			Hopf algebras of dimension 16 Algebr. Represent. Theory 13 (2010), no. 4, 383-405. with G. García.
			Aportes a la clasificación de las álgebras de Hopf (PhD Thesis) Director N. Andruskiewitsch. Fa.M.A.F., U.N.C. (2012).