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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

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1572-9176
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The Arnon bases in the Steenrod algebra

Neşet Deniz TurgayORCID iD: http://orcid.org/0000-0002-3952-7817 / Ismet Karaca
Published Online: 2018-11-14 | DOI: https://doi.org/10.1515/gmj-2018-0076

Abstract

Let 𝒜=𝒜p be the modp Steenrod algebra, where p is a fixed prime and let 𝒜 denote the Bockstein-free part of 𝒜 at odd primes. Being a connected graded Hopf algebra, 𝒜 has the canonical conjugation χ. Using this map, we introduce a relationship between the X- and Z-bases of 𝒜. We show that these bases restrict to give bases to the well-known sub-Hopf algebras 𝒜(n-1), n1, of 𝒜.

Keywords: Steenrod algebra; monomial basis; Adem relations; Arnon basis; Wall basis; Hopf algebra; antipode

MSC 2010: 55S10; 55S05; 57T05

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About the article

Received: 2016-09-16

Revised: 2016-11-23

Accepted: 2016-12-05

Published Online: 2018-11-14


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0076.

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