On order units in the augmentation ideal

Mizerka, Piotr; Nowak, Piotr

doi:10.1090/proc/16699

On order units in the augmentation ideal
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by Piotr Mizerka and Piotr W. Nowak;

Proc. Amer. Math. Soc. 152 (2024), 1999-2005

DOI: https://doi.org/10.1090/proc/16699

Published electronically: March 1, 2024

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Abstract:

We study order units in the real group ring and the augmentation ideal, as well as in matrix algebras. We identify an infinite family of order units in the powers of the augmentation ideal, that includes the Laplacian, and show that these order units are naturally obtained via cohomological operations from natural diagonal order units in matrix algebras.

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