About

Associate Professor (Profesor Titular) at Universidade de Santiago de Compostela and researcher at CITMAga.

Principal Researcher of the project "Homology, Homotopy and Categorical Invariants in Groups and Non-Associative Algebras" (PID2024-155502NB-I00).

Forthcoming events

    Research Interests
  • Non-associative algebra
  • Categorical algebra
  • Category theory
  • Homological algebra
  • Computational algebra

Research

  • Published papers
  • Preprints
  • Organisation of events

2027

Categorical-algebraic aspects of Heyting semilattices. Joint work with J. R. A. Gray, M. A. Hoefnagel, T. Van der Linden, C. Vienne. Annals of Pure and Applied Logic, 178(1), 103823, (2027).

2026

A note on complete evolution algebras. Joint work with A. Pérez Rodríguez. Archiv der Mathematik, 126, 597–604, (2026).
Introducing the Taubin-Weingarten algorithm to compute second-order geometric descriptors in 3D point clouds. Joint work with A. Esmorís, M. Ladra, J.C. Cabaleiro, F. Fernández Rivera. Journal of Computational and Applied Mathematics, 485, 117569, (2026).

2025

Action accessible and weakly action representable varieties of algebras. Joint work with M. Mancini. Bollettino dell'Unione Matematica Italiana, 19, 367–374, (2025).
Noncommutative Poisson structure and invariants of matrices. Joint work with F. Eshmatov, R. Turdibaev. Advances in Mathematics, 469, 110212, (2025).
On the coordinate rings of Calogero-Moser spaces and the invariant commuting variety of a pair of matrices. Joint work with F. Eshmatov, Z. Normatov, R. Turdibaev. Results in Mathematics, 80, Article 68, (2025).
Weak representability of actions of non-associative algebras. Joint work with J. Brox, M. Mancini, T. Van der Linden, C. Vienne. Journal of Algebra, 669, 401–444, (2025).

2024

A universal Kaluzhnin–Krasner embedding theorem. Joint work with B. S. Deval and T. Van der Linden. Proceedings of the American Mathematical Society, 152(12), 5039–5053, (2024).
A characterisation of Lie algebras using ideals and subalgebras. Joint work with V. Dotsenko. Bulletin of the London Mathematical Society, 56(7), 2408–2423, (2024).

2022

On some properties of Lie-centroids of Leibniz algebras. Joint work with J. M. Casas. Bulletin of the Malaysian Mathematical Sciences Society, 45, 3499–3520, (2022).
The ring of invariants of pairs of 3 × 3 matrices. Joint work with Z. Normatov and R. Turdibaev. Journal of Algebra, 603(1), 201–212, (2022).
On the capability of Hom-Lie algebras. Joint work with J. M. Casas. Mediterranean Journal of Mathematics, 19, Article 86, (2022).

2021

Some generalisations of Schur's and Baer's theorem and their connection with homological algebra. Joint work with G. Donadze. Mathematische Nachrichten, 294(11), 2129–2139, (2021).
Algebras with representable representations. Joint work with M. Tsishyn, T. Van der Linden and C. Vienne. Proceedings of the Edinburgh Mathematical Society, 64(3), 555–573, (2021).
Actor of a crossed module of dialgebras via tetramultipliers. Joint work with J. M. Casas, R. F. Casado and E. Khmaladze. Hacettepe Journal of Mathematics and Statistics, 50(4), 1063–1078, (2021).
Algebraic exponentiation for Lie algebras. Joint work with J. R. A. Gray. Theory and Applications of Categories, 36(11), 288–305, (2021).

2020

Abelian extensions and crossed modules of Hom-Lie algebras. Joint work with J. M. Casas. Journal of Pure and Applied Algebra, 224, 987–1008, (2020).

2019

Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds. Joint work with E. Calviño-Louzao, E. García-Río, I. Gutiérrez-Rodríguez, R. Vázquez-Lorenzo. Journal de Mathématiques Pures et Appliquées, 130, 347–374, (2019).
A characterisation of Lie algebras amongst anti-commutative algebras. Joint work with T. Van der Linden. Journal of Pure and Applied Algebra, 223, 4857–4870, (2019).
A characterisation of Lie algebras via algebraic exponentiation. Joint work with T. Van der Linden. Advances in Mathematics, 341, 92–117, (2019).

2018

A note on split extensions of bialgebras. Joint work with T. Van der Linden. Forum Mathematicum, 30(5), 1089–1095, (2018).
A non-abelian exterior product and homology of Leibniz algebras. Joint work with G. Donadze and E. Khmaladze. Revista Matemática Complutense, 31(1), 217–236, (2018).
Actor of a crossed module of Leibniz algebras. Joint work with J. M. Casas, R. F. Casado and E. Khmaladze. Theory and Applications of Categories, 33(2), 23–42, (2018).
Universal central extensions of Lie-Rinehart algebras. Joint work with J. L. Castiglioni and M. Ladra. Journal of Algebra and Its Applications, 17(7), 1850134, (2018).
Do n-Lie algebras have universal enveloping algebras? Joint work with R. Turdibaev and T. Van der Linden. Journal of Lie Theory, 28(1), 43–55, (2018).

2017

Universal central extensions of sl(m, n, A) of small rank over associative superalgebras. Joint work with M. Ladra. Turkish Journal of Mathematics, 41(6), 1552–1569, (2017).
A natural extension of the universal enveloping algebra functor to crossed modules of Leibniz algebras. Joint work with R. F. Casado and M. Ladra. Applied Categorical Structures, 25(6), 1059–1076, (2017).
A new characterisation of groups amongst monoids. Applied Categorical Structures, 25(4), 659–661, (2017).
Universal central extensions of Leibniz superalgebras over superdialgebras. Joint work with M. Ladra. Mediterranean Journal of Mathematics, 14(2), 14:73, (2017).

2016

Universal enveloping crossed module of Leibniz crossed modules and representations. Joint work with R. F. Casado and M. Ladra. Journal of Physics: Conference Series, 697, (2016).

2015

Non-abelian tensor product and homology of Lie Superalgebras. Joint work with E. Khmaladze and M. Ladra. Journal of Algebra, 440, 464–488, (2015).
Observations on the variety of equationally linear Heyting semilattices. Joint work with J. R. A. Gray, M. A. Hoefnagel, T. Van der Linden, C. Vienne. arXiv:2609.24325.
A comparison between weakly protomodular and protomodular objects in unital categories. Joint work with A. Montoli, D. Rodelo, T. Van der Linden. arXiv:2409.19076.
Categorical, homological and computational methods in Algebra. A conference in honour of Manuel Ladra Santiago de Compostela, Spain. 24th – 26th of June, 2026.
International Category Theory Conference CT2024 Santiago de Compostela, Spain. 23rd – 29th of June, 2024.
EACA Sixth International School on Computer Algebra and its Applications Santiago de Compostela, Spain. 18th – 21st of July, 2023.
Métodos Categóricos y Homotópicos en Álgebra, Geometría y Topología Santiago de Compostela, Spain. 5th – 6th of July, 2019.
24th Conference on Applications of Computer Algebra Santiago de Compostela, Spain. 18th – 22nd of June, 2018.
EACA Fourth International School on Computer Algebra and its Applications Santiago de Compostela, Spain. 20th – 23rd of March, 2018.
102nd Peripatetic Seminar on Sheaves and Logic Santiago de Compostela, Spain. 13th – 14th of January, 2018.
4th Spanish Young Topologists Meeting Santiago de Compostela, Spain. 20th – 23rd of October, 2014.

Education

PhD in Mathematics 2013 - 2017

University of Santiago de Compostela

My PhD thesis

Master degree in Mathematics 2012 - 2013

Universities of Santiago de Compostela & Porto

My Master thesis

Bachelor's degree in Mathematics 2008 - 2012

University of Santiago de Compostela

My Bachelor thesis

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