Algebra, Geometry

Rui Miguel Nobre Martins Pacheco

Ana Catarina dos Santos Carapito
Deolinda Isabel de Conceição Mendes
Henrique José Freitas da Cruz
Nuno Miguel Ferreira Correia
Patrícia Damas Beites
Rogério Pedro Fernandes Serôdio 


Manuel Almeida Silva
Sérgio Moço Mendes
André Bernardino
Isabel Maria Romano da Cunha Dias
Pedro Jorge Duarte Gil Morais
Ilda Carla Mendes Inácio Rodrigues  

    This reasearch group develops its activities in Linear and Multilinear Algebra, Combinatorics, Rings and Algebras, Differential Geometry and Control Theory, with emphasis in the following topics:

  • Harmonic maps from Riemann surfaces into Lie groups and associated families of integrable surfaces;
  • Submanifold Geometry;  
  • Almost periodic structures (the quasicrystals in physics) from different perspectives: word combinatorics, Ramsey theory, discrete geometry, dynamical systems and ergodic theory; 
  • The structure and radical theoretical properties of some classes of non-commutative associative rings; 
  • Symmetry classes of tensors and combinatorial parameters of matrices with positive entries; 
  • Structural properties of Switched Linear Systems; 
  • Composition and quaternion algebras over finite fields.



I. Brás, A. C. Carapito, P. Rocha. A note on simultaneous block diagonally stable matrices, ELA-The Electronic Journal of Linear Algebra, 26, 2013, 90-100.

I. Brás, A. C. Carapito, P. Rocha: Stability of Switched Systems With Partial State Reset, IEEE Transactions on Automatic Control, 58, 2013, 1008-1012.

R. Pacheco and H. Vilarinho. Metrics on tiling spaces, local isomorphism and an application of Brown's Lemma. Monatshefte für Mathematik, 170 (2), 2013, 205-225.

R. Pacheco and H. Vilarinho. Statistical Stability for Multi-Substitution Tiling Spaces. Discrete and Continuous Dynamical Systems – A, 33 (10), 2013, 4579-4594.

R. Pacheco, Immersed surfaces in Lie algebras associated to primitive harmonic maps, Geometriae Dedicata 163, 379-390, 2013.

R. Pacheco, Index and nullity of a family of harmonic tori in the sphere, Advances in Geometry, Volume 13, Issue 13, 381-388, 2013.


Correia, N. and Pacheco, R., Harmonic maps of finite uniton number into G2, Math. Z. 271 (1-2) (2012), 13-32.

Mendes, D.I.C. (2012). On completely *-prime *-ideals in involution rings, Mathematica Pannonica 23/2, 299-310


Beites, P. D., Nicolás, A. P., Pozhidaev, A. P. and Saraiva, P., On the identities of a ternary quaternion algebra, Communications in Algebra 39 (3) (2011), 830-842.

Correia, N. and Pacheco, R., Singular dressing actions on harmonic maps, Q. J. Math. 62 (1) (2011), 71–85.

Pacheco, R., Pinheiro, F. and Portugal, R., A note on the geometry of three circles, Creat. Math. Inform. 20 (1) (2011), 74-80.

Rostami, M. and Rodrigues, I.I., An observation on Krull and derived dimensions of some topological lattices, Archivum Mathematicum 47 (4) (2011), 329-334.

Serôdio, R., On the structure of quaternion rings over Zp, International Journal of Algebra 5 (27) (2011), 1313-1325.


Cecília Costa, M.A. Facas Vicente, Patrícia Beites, Fernando Martins, Rogério Serôdio e Pedro Tadeu (2010) Produto vectorial em R^7: Projecção de um ponto sobre uma recta, Boletim da Sociedade Portuguesa de Matemática, (62), 19--35.

Costa, C., Martins, F., Serôdio, R., Tadeu, P., Facas Vicente, M.A. e Vitória , J. , Conjugacy and Geometry II – Moore-Penrose Inverse and Feet of the Perpendiculars”, Far East Journal of Mathematical Education 4 (2010), 25-48.

Mendes, D.I.C., On involution rings with unique minimal *-subring, Beiträge zur Algebra und Geometrie 51 (2010), 137-146.

Pacheco, R., Bianchi-Bäcklund transforms and dressing actions, Geometriae Dedicata 146 (2010), 85-99.

Rostami, M., A symmetry extension of Steinitz’s Lemma on Polyhedra, Journal of Geometry and Topology (to appear).

Serôdio, R. (2010). Construction of octonionic polynomials, Advances in Applied Clifford Algebras 20 (1), 155-178.


Correia, N. and Pacheco, R. (2009) Adding a uniton via DPW method. International Journal of Mathematics. 20 (8), 997-2010.

Cortez, J., Mena Marugán, G., Serôdio, R. and Velhinho, J.M. (2009) Uniqueness of the Fock quantization of a free scalar field on S1 with time dependent mass, Phys. Rev. D 79 (8).

Costa, C., Martins, F., Serôdio, R., Tadeu, P., M.A. Facas Vicente, M.A. and Vitória, J. (2009). Conjugacy and geometry I – Foot of the perpendicular, distance and Gram determinant, Far East Journal of Mathematical Education, 3 (3), 235-262.

Cunha, I. and Elduque, A. (2009). The supermagic Square in characteristic 3 and Jordan superalgebras, Comtemporary Mathematics, 483, 91-106.

Dajczer, M. and Morais, P. (2009) Isometric rigidity in codimension 2, Michigan Math. Journal, Vol. 58, Issue 3, 759-770.

Mendes, D.I.C (2009) Minimal *-biideals of involution rings, Acta Sci. Math. (Szeged), vol. 75, 487-491.

Mendes, D.C.M. (2009) A note on involution rings, Miskolc Mathematical Notes, 10 (2), 155-162, 2009.

Pacheco, R. (2009) On harmonic tori in compact rank one symmetric spaces. Differential Geometry and its Applications. 27 (3), 335-354.

Rostami, M. (2009) On Dimensions of Spectral spaces of Finite Lattices. International Mathematical Forum, 4, (42), 2059 – 2063.


Beites, P.D. and Pozhidaev, A.P. (2008) On simple Filippov superalgebras of type A(n,n), Asian-European Journal of Mathematics, 1 (4), 469--487.

Breda, A., Marques, R.E., Rostami, M. e Wegner, B. (2008). On a classification of locally 2-Sierpinski spaces. Missouri Journal of Mathematical Sciences, 20(1), 53-59.

Pereira, E., Serôdio, R., Vitória, J. Newton's method for matrix polynomials. Int. J. Math. Game Theory Algebra 17, No. 4, 183-188 (2008)

Rostami, M., Wegner, B. e Breda, A. (2008). Locally n-Sierpinski spaces as subspaces of Sierpinski powers. IJMM-International Journal Mathematical Manuscripts, 2(1).

Rostami, M. (2008). On dimension of the manifold of polyhedral G-spaces. Int. J. Contemp. Math. Sciences, 3(11), 537-544.

Tumurbat, S., Mendes, D.I.C. e Mekei, A. (2008). On radicals and polynomial rings. Portugaliae Mathematica,vol 65, Issue 2, 261-273 . 


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