About

I obtained my PhD in Mathematics at Universidade de Santiago de Compostela, Spain, under the supervision of Manuel Ladra (Universidade de Santiago de Compostela) and Tim Van der Linden (Université Catholique de Louvain). I am currently an Assistant Professor at Universidade de Vigo and a postdoctoral researcher at Vrije Universiteit Brussel.

Forthcoming events

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

Research

  • Published papers
  • Preprints
  • Organisation of events
  • Participation in conferences
On the capablility of Hom-Lie algebras. Joint work with J. M. Casas. To appear in Mediterranean Journal of Mathematics, (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).
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).
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 alternating 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).
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 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).
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).
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).
Non-abelian tensor product and homology of Lie Superalgebras. Joint work with E. Khmaladze and M. Ladra. Journal of Algebra, 440, 464–488, (2015).
On some properties of Lie-centroids of Leibniz algebras. Joint work with J. M. Casas. arXiv:2107.08210.
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-22th 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-20rd of October, 2014.
National meeting of the SPM. Algebras with representable representations. Portugal. July 2021.
Taller de geometría diferencial. Bases de Gröbner. Universidad de Colima, México. July 2021.
EACA Tapas seminar on Computer Algebra. Gröbner bases in categorical algebra and differential geometry. Universidade de Santiago de Compostela. June 2021.
III International Workshop on Non-Associative Algebras. Actions in non-associtaive algebras. Universidad de Málaga. February 2020.
Seminar of Commutative Algebra and Algebraic Geometry. On two characterisations of Lie algebras. CIMAT, Guanajuato, Mexico. August 2019.
Operads and higher structures in Algebraic Topology and Category Theory. On two characterisations of Lie algebras. University of Ottawa, Canada. August 2019.
Categorical Methods in Algebra (satellite event of the 105th PSSL). A characterisation of Lie algebras via algebraic exponentiation. Universitá degli Studi di Palermo, Italy. May 2019.
Talks in the Mathematics Department of the UC. Categorical characterisation of algebraic structures. Universidad de Cantabria, Santander, Spain. May 2019.
II International Workshop on Non-Associative Algebras. Characterising algebraic structures via categorical properties. Universidade do Porto, Portugal. April 2019.
Talks in the Mathematics Department of the UNLP. Algebraic characterisation of categorical structures. Universidad de la Plata, Argentina. November 2018.
CT 2018 International Category Theory Conference. A categorical characterisation of Lie algebras. Universidade dos Açores, Ponta Delgada, Portugal. July 2018.
4th Workshop on Categorical Algebra. A characterisation of Lie algebras via algebraic exponentiation. Universitá degli Studi di Milano, Gargnano, Italy. May 2018.
Algebraic Groups and Related Areas Seminar. An introduction to categorical algebra. Northeast Normal University, Changchun, China. April - May 2018.
Non-associative Algebras in Cádiz. A categorical characterisation of Lie algebras. Universidad de Cádiz, Spain. February 2018.
CT 2017 International Category Theory Conference. A characterisation of Lie algebras amongst alternating algebras. University of the British Columbia, Vancouver, Canada. July 2017.
Categorical and Homotopical Methods in Algebra, Geometry and Topology. Split extensions of bialgebras. Universidad de Málaga, Spain. June 2017.
IV Joint meeting RSME-SMM. Split extensions of monoids and bialgebras. Universidad de Valladolid, Spain. June 2017.
5th Workshop of Cathegorical-methods in Non-abelian Algebra. Split extensions of bialgebras. Université Catholique de Louvain, Belgium. June 2017.
Modern Algebra and its Applications. Finding a categorical characterization of groups amongst monoids. National University of Uzbekistan after Mirzo Ulugbek, Tashkent, Uzbekistan. April 2017.
Category Theory Seminar. Lie objects are LACC. Université Catholique de Louvain, Belgium. April 2017.
Category Theory Days 2017. LACC categories of non-associative algebras. Stellenbosch University, South Africa. March 2017.
Mathematical Structures Seminar. Finding a categorical-algebraic characterization of Groups amongst Monoids. Stellenbosch University, South Africa. November 2016.
6th Iberian Mathematical Meeting. The non-abelian tensor product of different structures. Universidade de Santiago de Compostela, Spain. October 2016.
XV EACA 2016: Computational Algebra and Applications Meeting. The universal enveloping algebra of an n-Lie algebra. Universidad de La Rioja, Spain. June 2016.
EACA's Third International School on Computer Algebra and Applications. The universal enveloping algebra in the category of n-Lie algebras. Universidad de Sevilla, Spain. January 2016.
Lie and Jordan Algebras, Their Representations and Applications VI. Non-abelian tensor product of Lie superalgebras. Universidade de São Paulo, Bento Gonçalves, Brazil. December 2015.
First Joint Meeting Brazil-Spain in Mathematics. Universal central extensions of Lie-Rinehart algebras. Universidade Federal do Ceará, Fortaleza, Brazil. December 2015.
Algebra, Analysis and Quantum Probability. The universal enveloping algebra in the category of n-Lie algebras. National University of Uzbekistan after Mirzo Ulugbek, Tashkent, Uzbekistan. September 2015.
4rd Spanish Young Topologist Meeting. Operads and enveloping algebras. Universidad Politecnica de Madrid, Spain. June 2015.
Joint International Meeting of the American, European and Portuguese Mathematical Societies. Universal central extensions of Lie-Rinehart algebras. Universidade do Porto, Portugal. June 2015.
UCL-ULB-VUB joint Category Theory Seminar. Do n-Lie algebras have universal enveloping algebras? Université Catholique de Louvain, Belgium. June 2015.
Biennial RSME Congress 2015. Universal central extensions of Lie-Rinehart algebras. Universidad de Granada, Spain. February 2015.
Non-associative Algebra and Lie Theory. Universal central extensions of Lie-Rinehart algebras. Universidad Nacional Autónoma de Mexico, Oaxaca, Mexico. January 2015.
International Congress of Mathematicians. Non-abelian tensor product of Lie Superalgebras. Seoul, South Korea. August 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