We use the connection between supercharacter theories and Schur rings described by Hendrickson in [5] to reconstruct the supercharacter theory developed by André, Freitas and Neto in [3] for fixed point subgroups arising from involutions defined on algebra groups, aiming to simplify the process.
Main references:
[1] C.A.M. André, Supercharacters of unitriangular groups and set partition combinatorics, ECOS2013, CIMPA school (notes of the course).
[2] C.A.M. André, A.P. Nicolás, Supercharacters of the adjoint group of a finite radical ring, J. Group Theory 11 (2008), 709-746.
[3] C. A. M. André, P. J. Freitas, A. M. Neto, A supercharacter theory for involutive algebra groups, J. Algebra 430 (2015), 159–190.
[4] P. Diaconis, I.M. Isaacs, Supercharacters and superclasses for algebra groups, Trans. Amer. Math. Soc. 360 (2008), 2359-2392.
[5] A.O.F. Hendrickson, Supercharacter theory constructions corresponding to Schur ring products, Comm. Algebra 40 (2012), no.12, 4420-4438.
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