Bivariate polynomial mappings associated with simple complex Lie algebras

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2016-11-01
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.

Citation Formats
Ö. Küçüksakallı, “Bivariate polynomial mappings associated with simple complex Lie algebras,” JOURNAL OF NUMBER THEORY, vol. 168, pp. 433–451, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39430.