Current research

• Determination and classification of set-theoretical solutions to the Yang-Baxter equation, a basic equation of Statistical Mechanics. Our investigation is strictly linked to the study of specific algebraic structures, such as braces, skew braces, cycle sets, and their generalizations.

• Investigation of the polynomial identities in group algebras, enveloping algebras, and some related structures (in particular, smash products and symmetric Poisson algebras), with special attention to Lie identities satisfied by these algebraic structures. 

• Interest in some topics concerning cohomology, representation theory, and the subalgebra lattice of restricted Lie algebras. 

• Study of set-theoretical solutions of the pentagon equation, a well-known equation of modern Mathematical Physics,  on specific classes of semigroups.

• Description of regular subgroups of the affine group of a vector space using the link between regular subgroups and radical F-braces.

Preprints 

1. A. Albano, M. Mazzotta, P. Stefanelli: Reflections to set-theoretic solutions of the Yang-Baxter equation, preprint arXiv https://arxiv.org/abs/2405.19105 

2. M. Mazzotta, B. Rybołowicz, P. Stefanelli: Deformed solutions of the Yang-Baxter equation associated to dual weak braces,  preprint arXiv https://arxiv.org/abs/2304.05235 

3. A. Doikou, B. Rybołowicz, P. Stefanelli: Quandles as pre-Lie skew braces, set-theoretic Hopf algebras & universal R-matrices, preprint arXiv https://arxiv.org/pdf/2401.12704.pdf 

Recent publications (since 2020)

In press

1. P. Páez-Guillán, S. Siciliano, D. Towers: Modularity conditions in Leibniz algebras, accepted for publication in Journal of Algebra and Its Applications (2024).

Accepted for publication

1. M. Mazzotta: Set-theoretical solutions of the pentagon equation: a survey,  accepted for publication in Communications in Mathematics, Volume 33 (2025), Issue 3 (Special issue: European Non-Associative Algebra Seminar).

2. P. Stefanelli: Dual weak braces and Płonka sums of solutions of the Yang-Baxter equation, Proceedings LOOPS'23, Będlewo, Banach Center Publications, Institute of Mathematics, Polish Academy of Sciences, Warszawa.

3. M. Mazzotta: A family of set-theoretic solutions of the Yang-Baxter equation coming from skew braces, Proceedings LOOPS'23, Będlewo, Banach Center Publications, Institute of Mathematics, Polish Academy of Sciences, Warszawa.

2024

1. M. Mazzotta: Idempotent set-theoretical solutions of the pentagon equation, Boll. Unione Mat. Ital.  17 , 457-469 (2024),  https://doi.org/10.1007/s40574-023-00382-8

2. M. Mazzotta, V. Pérez-Calabuig, P. Stefanelli: Set-theoretical solutions of the pentagon equation on Clifford semigroups, Semigroup Forum 108(2) (2024), 413-431, https://doi.org/10.1007/s00233-024-10421-1

3. F. Catino, M. Mazzotta, P. Stefanelli: Solutions of the Yang-Baxter equation and strong semilattices of skew braces, Mediterr. J. Math., 2024, 21(2), 67, https://doi.org/10.1007/s00009-024-02611-6

4. M. Khrypchenko, S. Siciliano: Identities and derived lengths of finitary incidence algebras and their group of units, Comm. Algebra, 2024, 52(2), pp. 916–922,  https://doi.org/10.1080/00927872.2023.2253464 

2023

5. P. Stefanelli: Semi-affine structures on groups and semi-braces, J. Pure Appl. Algebra 227 (2023), no. 9, Paper No. 107383, 19 pp. https://doi.org/10.1016/j.jpaa.2023.107383

6. N. Maletesta, S. Siciliano: Five-dimensional p-nilpotent restricted Lie algebras over algebraically closed fields of characteristic p > 3, Journal of Algebra, 2023, 634, pp. 755–789. https://doi.org/10.1016/j.jalgebra.2023.05.029 

7. F. Catino, M. Mazzotta, P. Stefanelli: Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equation,  J. Algebra 622 (2023) 587–613, https://doi.org/10.1016/j.jalgebra.2023.02.013 

8. P. Páez-Guillán, S.Siciliano, D.A.Towers: On the subalgebra lattice of a restricted Lie algebra, Linear Algebra and Its Applications (2023) 660, pp. 47–65, https://doi.org/10.1016/j.laa.2022.12.004 

2022

1. S. Siciliano, D.A. Towers: On the subalgebra lattice of a Leibniz algebra, Communications in Algebra (2022) 50(1), pp. 255–267. https://doi.org/10.1080/00927872.2021.1956510 

2. N. Maletesta, P. Páez-Guillán, S. Siciliano: Restricted Lie algebras having a distributive lattice of restricted subalgebras, Linear Multilinear Algebra 69 (2021), no. 16, 3112–3120. https://doi.org/10.1080/03081087.2019.1708238 

3. M. Castelli, M. Mazzotta, P. Stefanelli: Simplicity of indecomposable set-theoretic solutions of the Yang-Baxter equation,  Forum Math., 34 (2022) no. 2, 531–546. https://doi.org/10.1515/forum-2021-0189

4. F. Catino, M. Mazzotta, M.M. Miccoli, P. Stefanelli: Set-theoretic solutions of the Yang-Baxter equation associated to weak braces, Semigroup Forum 104 (2) (2022) 228–25.  https://doi.org/10.1007/s00233-022-10264-8

5. F. Catino, F. Cedó, P. Stefanelli: Nilpotency in left semi-braces, J. Algebra 604 (2022), 128–161. https://doi.org/10.1016/j.jalgebra.2022.04.004 

6. M. Castelli, F. Catino, P. Stefanelli: Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and dynamical extensions of q-cycle sets, J. Algebra Appl., 21 (2022), no. 8, Paper No. 2250154. https://doi.org/10.1142/S0219498822501547

2021

1. S. Siciliano,  H. Usefi: On a conjecture about solvability of symmetric Poisson algebras, Bull. Lond. Math. Soc. (2021). doi.org/10.1112/blms.12479

2. S. Siciliano, D. Towers: On the subalgebra lattice of a Leibniz algebra, Comm. Algebra (2021). doi.org/10.1080/00927872.2021.1956510

3. F. Catino, M. Mazzotta, P. Stefanelli: Inverse semi-braces and the Yang-Baxter equation, J. Algebra 573 (2021) 576–619. https://doi.org/10.1016/j.jalgebra.2021.01.009 

4. S. Siciliano, H. Usefi: Solvability of Poisson algebras, J. Algebra 568 (2021), 349–361. https://doi.org/10.1016/j.jalgebra.2020.10.012 

5. F. Catino, I. Colazzo, P. Stefanelli: Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces, Forum Math., 33 (2021), no. 3, 757–772. https://doi.org/10.1515/forum-2020-0082 

6. M. Castelli, F. Catino, P. Stefanelli, Indecomposable Involutive Set-Theoretic Solutions of the Yang-Baxter Equation and Orthogonal Dynamical Extensions of Cycle Sets, Mediterr. J. Math. 18 (2021), no. 6, 246. https://doi.org/10.1007/s00009-021-01912-4 

2020

1. S. Siciliano: Solvable symmetric Poisson algebras and their derived lengths, J. Algebra 543 (2020), 98–110. https://doi.org/10.1016/j.jalgebra.2019.10.017 

2. F. Catino, M. Mazzotta, P. Stefanelli: Set-theoretical solutions of the Yang-Baxter and pentagon equations on semigroups, Semigroup Forum 100 (3) (2020) 1–26. https://doi.org/10.1007/s00233-020-10100-x 

3. M. Castelli, G. Pinto, W. Rump, On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size, Comm. Algebra 48 (5) (2020) 1941–1955. https://doi.org/10.1080/00927872.2019.1710163 

4. F. Catino, M. Mazzotta, M.M. Miccoli: Set-theoretical solutions of the pentagon equation on groups, Comm. Algebra 48 (2020) 83–92. https://doi.org/10.1080/00927872.2019.1632331 

5. F. Catino, I. Colazzo, P. Stefanelli: The Matched Product of the Solutions to the Yang–Baxter Equation of Finite Order, Mediterr. J. Math. 17, 58 (2020) https://doi.org/10.1007/s00009-020-1483-y 

6. F. Catino, I. Colazzo, P. Stefanelli: The matched product of set-theoretic solutions of the Yang-Baxter equation, J. Pure Appl. Algebra 224 n.3 (2020), 1173–1194 https://doi.org/10.1016/j.jpaa.2019.07.012