Journal of Group Theory ( IF 0.466 ) Pub Date : 2020-08-25 , DOI: 10.1515/jgth-2020-0049
Alberto Cassella; Claudio Quadrelli

Let 𝔽 be a finite field. We prove that the cohomology algebra $H∙⁢(GΓ,F)$ with coefficients in 𝔽 of a right-angled Artin group $GΓ$ is a strongly Koszul algebra for every finite graph Γ. Moreover, $H∙⁢(GΓ,F)$ is a universally Koszul algebra if, and only if, the graph Γ associated to the group $GΓ$ has the diagonal property. From this, we obtain several new examples of pro-𝑝 groups, for a prime number 𝑝, whose continuous cochain cohomology algebra with coefficients in the field of 𝑝 elements is strongly and universally (or strongly and non-universally) Koszul. This provides new support to a conjecture on Galois cohomology of maximal pro-𝑝 Galois groups of fields formulated by J. Mináč et al.

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