Research Interests

Algebra

Non-associative algebras (Lie algebras, Leibniz algebras), derivations of non-associative algebras and related topics (e.g., biderivations).

Geometry

Lie theory, smooth manifolds, Lie groups, Lie racks, and the coquecigrue problem.

Logic

Fuzzy set theory, fuzzy logic, and fuzzy abstract algebra (e.g., fuzzy vector spaces, fuzzy Lie algebras).

Knowledge Representation

Building ontologies for AI implementations (e.g., Natural Language Processing), and fuzzy reasoning in crisp ontologies (e.g., FuzzyOWL 2).

Publications

Preprints

  1. Biderivations of complete Leibniz algebras (with A. Di Bartolo and F. P. Di Fatta), arXiv:2510.16426
  2. A Lie Bracket on the Space of (Right) Biderivations of a Lie Algebra (with A. Di Bartolo), arXiv:2507.12089
  3. A New Definition of Superbiderivations for Lie Superalgebras (with A. Di Bartolo and F. P. Di Fatta), arXiv:2506.23710

Journal Articles

  1. Flag Manifolds without One Codimensional Strata (with A. Di Bartolo), accepted for publication in Differential Geometry of Manifolds of Figures, ISSN: 0321-4796
  2. Fuzzy MCGDM Approach for Ontology Fuzzification (with L. Castronovo, G. Filippone, M. Galici, and M. E. Tabacchi), in Electronics 14.18 (2025), doi: 10.3390/electronics14183596
  3. On a class of two-step solvable Leibniz algebras (with A. Di Bartolo), in International Journal of Algebra and Computation 35.05 (2025), pp. 733–758, doi: 10.1142/S0218196725500249
  4. Biderivations of complete Lie algebras (with A. Di Bartolo), in Journal of Algebra and Its Applications 24.01 (2025), p. 2550016, doi: 10.1142/S0219498825500161
  5. Non-Nilpotent Leibniz Algebras with One-Dimensional Derived Subalgebra (with A. Di Bartolo and M. Mancini), in Mediterranean Journal of Mathematics 21 (2024), p. 138, doi: 10.1007/s00009-024-02679-0
  6. Isotopisms of nilpotent Leibniz algebras and Lie racks (with M. Mancini and G. P. Nagy), in Communications in Algebra 52.9 (2024), pp. 3812–3825, doi: 10.1080/00927872.2024.2330686
  7. Derivations of two-step nilpotent algebras (with M. Mancini), in Communications in Algebra 51.12 (2023), pp. 4928–4948, doi: 10.1080/00927872.2023.2222415
  8. Two-step nilpotent Leibniz algebras (with M. Mancini), in Linear Algebra and its Applications 637 (2022), pp. 119–137, doi: 10.1016/j.laa.2021.12.013

Conference Papers

  1. SDF FuzzIA: A fuzzy-based, AI support system for decision-making frameworks (with L. Castronovo, G. Filippone, M. Galici, A. M. Pavone, and M. E. Tabacchi), accepted for proceedings of International Summer Conference 2025 (ISC25), Lecture Notes in Computer Science, Springer Nature Switzerland, 2025
  2. A new definition of fuzzy nilpotent Lie algebras (with G. Filippone, M. Galici, F. Piazza, and M. E. Tabacchi), in 2025 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1–5, doi: 10.1109/FUZZ62266.2025.11152208
  3. Some Results on Fuzzy Basis of Fuzzy Lie Algebras (with G. Filippone, M. Galici, and M. E. Tabacchi), in Advances in Fuzzy Logic and Technology, Ed. by Michał Baczyński, Bernard De Baets, Michal Holčapek, Vladik Kreinovich and Jesús Medina, Cham: Springer Nature Switzerland, 2025, pp. 98–109, ISBN: 978-3-031-97228-7, doi: 10.1007/978-3-031-97228-7_9
  4. Ontology Aggregation with Maximum Consensus Based on a Fuzzy Multi-criteria Group Decision-Making Method (with L. Castronovo, G. Filippone, M. Galici, and M. E. Tabacchi), in Advances in Fuzzy Logic and Technology, Ed. by Michał Baczyński, Bernard De Baets, Michal Holčapek, Vladik Kreinovich and Jesús Medina, Cham: Springer Nature Switzerland, 2025, pp. 76–87, ISBN: 978-3-031-97228-7, doi: 10.1007/978-3-031-97228-7_7
  5. Fuzziness and Lie Algebras (with G. Filippone, M. Mancini, and M. E. Tabacchi), in Information Processing and Management of Uncertainty in Knowledge-Based Systems, Ed. by Marie-Jeanne Lesot, Susana Vieira, Marek Z. Reformat et al., Cham: Springer Nature Switzerland, 2025, pp. 113–123, ISBN: 978-3-031-74000-8, doi: 10.1007/978-3-031-74000-8_10
  6. Max Black and a Logic of Vagueness (with G. Filippone and M. E. Tabacchi), in Information Processing and Management of Uncertainty in Knowledge-Based Systems, Ed. by Marie-Jeanne Lesot, Susana Vieira, Marek Z. Reformat et al., Cham: Springer Nature Switzerland, 2025, pp. 105–112, ISBN: 978-3-031-74000-8, doi: 10.1007/978-3-031-74000-8_9
  7. SDF-FuzzIA: A Fuzzy-Ontology Based Plug-in for the Intelligent Analysis of Geo-Thematic Data (with G. Filippone and M. E. Tabacchi), in Scalable Uncertainty Management, Ed. by Sébastien Destercke, Maria Vanina Martinez and Giuseppe Sanfilippo, Cham: Springer Nature Switzerland, 2025, pp. 163–169, ISBN: 978-3-031-76235-2, doi: 10.1007/978-3-031-76235-2_13

PhD Thesis

  • On nilpotent Leibniz algebras, Lie biderivations and related topics, 2024, link