On Additive Bases and Change of Bases in $\mathbb C$-Motivic Steenrod Algebra mod 2

Th. Yu. Popelensky<sup>abc

a</sup> Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
^c National Research University Higher School of Economics (HSE University), Moscow, Russia

Abstract: We construct additive bases over $\mathbb M_2=\mathbb Z/2[\tau ]$ for the mod $2$ motivic Steenrod algebra and characterize those bases for which the transition matrix to the Milnor basis is triangular with respect to suitable linear orders on the sets of basis elements.

Keywords: motivic Steenrod algebra, Adem relations, admissible basis, Milnor basis, change of bases.

Received: May 5, 2025
Revised: June 2, 2025
Accepted: July 16, 2025

DOI: 10.4213/tm4484

 English version: Proceedings of the Steklov Institute of Mathematics, 2025, 330, 301–313

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