# On realizations of the subalgebra $A^R(1)$ of the $R$-motivic Steenrod Algebra

@inproceedings{Bhattacharya2021OnRO, title={On realizations of the subalgebra \$A^R(1)\$ of the \$R\$-motivic Steenrod Algebra}, author={Prasit Bhattacharya and Bertrand J. Guillou and Ang Li}, year={2021} }

. In this paper, we show that the ﬁnite subalgebra A R (1), generated by Sq 1 and Sq 2 , of the R -motivic Steenrod algebra A R can be given 128 diﬀerent A R -module structures. We also show that all of these A -modules can be realized as the cohomology of a 2-local ﬁnite R -motivic spectrum. The realization results are obtained using an R -motivic analogue of the Toda realization theorem. We notice that each realization of A R (1) can be expressed as a coﬁber of an R -motivic v 1 -self-map…

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