Bivariate polynomial mappings associated with simple complex Lie algebras

2016/01/26 by Ömer Küçüksakallı, Küçüksakallı, Ömer
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1601.07132

16 pages, 6 figures

arxiv created 2016/01/26 · arxiv updated 2016/01/27

Abstract

There are three families of bivariate polynomial maps associated with the rank-2 simple complex Lie algebras A₂, B₂ ≅ C₂ and G₂. It is known that the bivariate polynomial map associated with A₂ induces a permutation of F_q² if and only if gcd(k,q^s-1)=1 for s=1, 2, 3. In this paper, we give similar criteria for the other two families. As an application, a counterexample is given to a conjecture posed by Lidl and Wells about the generalized Schur's problem.

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