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M. J. Pereira-Sáez

  1. An upper bound for the Lusternik-Schnirelmann category of the symplectic group.

    Tue, 02/28/2012 - 15:01 — SomNambul
    Authors: E. Macías-Virgós, M. J. Pereira-Sáez
    Subjects: Algebraic Topology
    Abstract

    We prove that the LS category of the symplectic group $Sp(n)$ is bounded
    above by $\binom{n+1}{2}$. This is achieved by computing the number of critical
    levels of a height function.

  2. Characteristic functions for left eigenvalues of quaternionic matrices.

    Wed, 05/05/2010 - 15:01 — SomNambul
    Authors: E. Macías-Virgós, M. J. Pereira-Sáez
    Subjects: Rings and Algebras
    Abstract

    We introduce the notion of characteristic function of a quaternionic matrix,
    whose roots are the left eigenvalues. We prove that for all $2\times 2$
    matrices and for $3\times 3$ matrices having some zero entry outside the
    diagonal there is a characteristic function which satisfies Hamilton-Cayley
    theorem.

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