Conjectures on the anti-automorphism of Z-basis of the Steenrod algebra

Journal of Linear and Topological Algebra

دوره 10، شماره 01، خرداد 2021، صفحه 11-18   

نوع مقاله: Research Paper

نویسندگان

T. Vergili^{* 1}؛ I. Karaca²

¹Department of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon, Turkey

²Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey

چکیده

In this paper, we compute the images  of some of the $Z$-basis elements under the anti-automorphism map $\chi$ of the mod 2 Steenrod algebra $\mathcal{A}_2$ and propose some conjectures based on our computations.

کلیدواژه‌ها

Steenrod Algebra؛ cohomology operations؛ conjugation map؛ Hopf Algebra

مراجع

[1] J. F. Adams, H. R. Margolis, Modules over the Steenrod algebra, Topology. 10 (1971), 271-282.

[2] D. Arnon, Monomial bases in the Steenrod algebra, J. Pure. Appl. Algebra. 96 (1994), 215-223.

[3] M. G. Barrat, H. Miller, On the anti-automorphism of the Steenrod algebra, Contemporary Math. 12 (1981), 47-52.

[4] D. M. Davis, The anti-automorphism of the Steenrod algebra, Proc. Amer. Math. Soc. 44 (1974), 235-236.

[5] I. Karaca, I. Y. Karaca, On conjugation in the Mod-p Steenrod Algebra, Turkish J. Math. 24 (2001), 1-7.

[6] I. Karaca, I. Y. Karaca, Some formulas for conjugation, Southwest J. Pure. Appl. Math. 2 (2001), 43-52.

[7] J. Milnor, The Steenrod algebra and its dual, Annals of Mathematics. 67 (1958), 150-171.

[8] J. P. Serre, Cohomologie module 2 des complexes d'Eilenberg-MacLane, Commentarii Mathematici Helvetici. 27 (1953), 198-232.

[9] J. Silverman, Conjugation and excess in the Steenrod algebra, Proc. Amer. Math. Soc. 119 (1993), 657-661.

[10] N. E. Steenrod, D. B. A. Epstein, Cohomology operations, Annals of Math Studies 50, Princeton University Press, 1962.

[11] N. D. Turgay, A remark on the conjugation in the Steenrod algebra, Commun. Korean. Math. Soc. 30 (3) (2015), 269-276.

[12] T. Vergili, I. Karaca, Examples of self-dual codes over some sub-Hopf algebras of the Steenrod algebra, Turkish J. Math. 47 (2017), 1313-1322.

[13] T. Vergili, I. Karaca, A note on the new basis in the mod 2 Steenrod algebra, J. Linear. Topological. Algebra. 7 (2) (2018), 101-107.

[14] R. M. W. Wood, A note on bases and relations in the Steenrod algebra, Bull. London. Math. Soc. 27 (1995), 380-386.

[15] R. M. W. Wood, Problems in the Steenrod algebra, Bull. London. Math. Soc. 30 (1998), 449-517.