Abstract
We present a classification of the so-called “additive symmetric 2-cocycles” of arbitrary degree and dimension over $\mathbb{F}_p$, along with a partial result and some conjectures for $m$-cocycles over $\mathbb{F}_p$, $m \gt 2$. This expands greatly on a result originally due to Lazard and more recently investigated by Ando, Hopkins and Strickland, and together with their work this culminates in a complete classification of $2$-cocycles over an arbitrary commutative ring. The ring classifying these polynomials finds application in algebraic topology, to be fully explored in a sequel.
Citation
Adam Hughes. Johnmark Lau. Eric Peterson. "A classification of additive symmetric 2-cocycles." Illinois J. Math. 53 (4) 983 - 1017, Winter 2009. https://doi.org/10.1215/ijm/1290435335
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