Right-angled Artin groups and enhanced Koszul properties

Abstract

Let F be a finite field. We prove that the cohomology algebra with coefficients in F of a right-angled Artin group is a strongly Koszul algebra for every finite graph $\Gamma$. Moreover, the same algebra is a universally Koszul algebra if, and only if, the graph $\Gamma$ associated to the right-angled Artin group 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 prop Galois groups of fields formulated by J. Mináč et al.

arXiv commentTo appear in J. Group Theory

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• Algebraic invariants for right-angled Artin groups
• The Kummerian Property and Maximal Pro-$p$ Galois Groups
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Cited by in corpus (3)

• Groups of p-absolute Galois type that are not absolute Galois groups
• Oriented right-angled Artin pro-$\ell$ groups and maximal pro-$\ell$ Galois groups
• Directed graphs, Frattini-resistance, and maximal pro-$p$ Galois groups