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Relations between modular invariants of a vector and a covector in dimension two

Part of: General commutative ring theory

Published online by Cambridge University Press:  28 October 2020

Yin Chen
Yin Chen*
Affiliation:
School of Mathematics and Statistics, Northeast Normal University, Changchun130024, China and Department of Mathematics and Statistics, Queen’s University, Kingston, K7L 3N6, Canada
*
e-mail:[email protected]
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Abstract

We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.

Keywords

Modular invariantsgeneral linear groupsfinite fields

MSC classification

Primary: 13A50: Actions of groups on commutative rings; invariant theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021 , pp. 820 - 827
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Copyright
© Canadian Mathematical Society 2020

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References

Bonnafé, C. and Kemper, G., Some complete intersection symplectic quotients in positive characteristic: invariants of a vector and a covector . J. Algebra 335(2011), 96–112. https://doi:10.1016/j.jalgebra.2011.03.007 CrossRefGoogle Scholar
Campbell, H. E. A., Hughes, I., and Pollack, R. D., Rings of invariants and $p$ -Sylow subgroups. Canad. Math. Bull. 34(1991), no. 1, 42–47. https://doi.org/10.4153/CMB-1991-007-0 Google Scholar
Chen, Y., On modular invariants of a vector and a covector . Manuscr. Math. 144(2014), nos. 3–4, 341–348. https://doi.org/10.1007/s00229-013-0648-4 CrossRefGoogle Scholar
Chen, Y. and Wehlau, D. L., Modular invariants of a vector and a covector: a proof of a conjecture of Bonnafé and Kemper . J. Algebra 472(2017), 195–213. https://doi.org/10.1016/j.jalgebra.2016.09.029 CrossRefGoogle Scholar
Derksen, H. and Kemper, G., Computational invariant theory . 2nd enlarged ed., Encyclopaedia of Mathematical Sciences, 130, Invariant Theory and Algebraic Transformation Groups, VIII, Springer, Heidelberg, 2015. https://doi.org/10.1007/978-3-662-48422-7 Google Scholar