Bivariate polynomial mappings associated with simple complex Lie algebras

Date

2016-11-01

Author

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

Collections

Department of Mathematics, Article