FMF in IMFM, Matematična knjižnica, Ljubljana (MAKLJ)
  • Endomorphisms of abelian groups with small algebraic entropy
    Dikranjan, Dikran N., 1950- ; Gong, Ketao ; Zanardo, Paolo
    We study the endomorphisms ▫$\phi$▫ of abelian groups ▫$G$▫ having a "small" algebraic entropy ▫$h$▫ (where "small" usually means ▫$h(\phi) < \log 2$▫. Using essentially elementary tools from linear ... algebra, we show that this study can be carried out in the group ▫$\mathbb{Q}^d$▫, where an automorphism ▫$\phi$▫ with ▫$h(\phi) < \log 2$▫ must have all eigenvalues in the open circle of radius 2, centered at 0 and ▫$\phi$▫ must leave invariant a lattice in ▫$\mathbb{Q}^d$▫, i.e., be essentially an automorphism of ▫$\mathbb{Z}^d$▫. In particular, all eigenvalues of an automorphism ▫$\phi$▫ with ▫$h(\phi) = 0$▫ must be roots of unity. This is a particular case of a more general fact known as Algebraic Yuzvinskii Theorem. We discuss other particular cases of this fact and we give some applications of our main results.
    Vir: Linear algebra and its applications. - ISSN 0024-3795 (Vol. 439, iss. 7, 2013, str. 1894-1904)
    Vrsta gradiva - članek, sestavni del
    Leto - 2013
    Jezik - angleški
    COBISS.SI-ID - 16798553

    Povezava(-e):

    http://dx.doi.org/10.1016/j.laa.2013.05.021

vir: Linear algebra and its applications. - ISSN 0024-3795 (Vol. 439, iss. 7, 2013, str. 1894-1904)

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