Bivariate polynomial mappings associated with simple complex Lie algebras

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2016-11-01

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Küçüksakallı, Ömer

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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.

Subject Keywords

Chebyshev polynomial, Dickson polynomial, Lie algebra, Weyl group, Integrable mapping, Exceptional polynomial, Schur's problem

URI

https://hdl.handle.net/11511/39430

Journal

JOURNAL OF NUMBER THEORY

DOI

https://doi.org/10.1016/j.jnt.2016.04.021

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Department of Mathematics, Article

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Citation Formats

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