Bivariate polynomial mappings associated with simple complex Lie algebras

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KÜÇÜKSAKALLI Ö.

JOURNAL OF NUMBER THEORY, vol.168, pp.433-451, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 168
  • Publication Date: 2016
  • Doi Number: 10.1016/j.jnt.2016.04.021
  • Journal Name: JOURNAL OF NUMBER THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.433-451
  • Middle East Technical University Affiliated: Yes

Abstract

There are three families of bivariate polynomial maps associated with the rank-2 simple complex Lie algebras A(2), B-2 congruent to C-2 and G(2). It is known that the bivariate polynomial map associated with A(2) induces a permutation of F-q(2) if and only if gcd(k, q(3) - 1) = I. 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. (C) 2016 Elsevier Inc. All rights reserved.