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  • Maps on upper triangular matrices preserving Lie products
    Dolinar, Gregor, 11.08.1971-
    Let ▫$\mathbb{F}$▫ be an arbitrary field with characteristic zero, let ▫$T_n$▫ be the Lie algebra of all ▫$n \times n$▫ upper triangular matrices over ▫$\mathbb{F}$▫ with the Lie product ▫$[A,B] = ... AB-BA$▫, and let a bijective map ▫$\varphi: T_n \to T_n$▫ satisfy ▫$\varphi([A,B]) = [\varphi(A), \varphi(B)]$▫, ▫$A,B \in T_n$▫ Then there exist an invertible matrix ▫$T \in T_n$▫, a function ▫$\varphi : T_n \to \mathbb{F}$▫ satisfying ▫$\varphi(C)=0$▫ for every strictly upper triangular matrix ▫$C \in T_n$▫ and an automorphism ▫$f$▫ of the field ▫$\mathbb{F}$▫, such that ▫$\phi([a_{ij}]) = T[f(a_{ij})]T^{-1} + \varphi([a_{ij}])I$▫ for all ▫$[a_{ij}] \in T_n$▫, or ▫$\phi([a_{ij}]) = -R(T[f(a_{ij})]T^{-1})^t R^{-1} + \varphi([a_{ij}])I$▫ for all ▫$[a_{ij}] \in T_n$▫, where ▫$R = \sum_{i=1}^n (-1)^i E_{1, n+1-i}$▫.
    Vir: Linear and Multilinear Algebra. - ISSN 0308-1087 (Vol. 55, no. 2, 2007, str. 191-198)
    Vrsta gradiva - članek, sestavni del
    Leto - 2007
    Jezik - angleški
    COBISS.SI-ID - 14212953

    Povezava(-e):

    http://dx.doi.org/10.1080/03081080600635484

vir: Linear and Multilinear Algebra. - ISSN 0308-1087 (Vol. 55, no. 2, 2007, str. 191-198)

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