Abstract
Let P k be the graded polynomial algebra \(\mathbb {F}_{2}[x_{1},x_{2},{\ldots } ,x_{k}]\) over the prime field of two elements, \(\mathbb {F}_{2}\), with the degree of each x i being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for P k as a module over the mod-2 Steenrod algebra, \(\mathcal {A}\). In this paper, we explicitly determine a minimal set of \(\mathcal {A}\)-generators for P k in the case k = 5 and the degree 4(2d−1) with d an arbitrary positive integer.
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Acknowledgments
The final version of this paper was completed while the second named author was visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM) from August to December 2015. He would like to thank the VIASM for financial support and kind hospitality. The work was supported in part by a grant of the NAFOSTED.
We would like to express our warmest thanks to the referee for the careful reading and helpful suggestions.
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Phuc, D.V., Sum, N. On a Minimal Set of Generators for the Polynomial Algebra of Five Variables as a Module over the Steenrod Algebra. Acta Math Vietnam 42, 149–162 (2017). https://doi.org/10.1007/s40306-016-0190-z
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DOI: https://doi.org/10.1007/s40306-016-0190-z