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Bivariate polynomial mappings associated with simple complex Lie algebras
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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
Journal
JOURNAL OF NUMBER THEORY
DOI
https://doi.org/10.1016/j.jnt.2016.04.021
Collections
Department of Mathematics, Article
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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.