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 Γ. Moreover, the same algebra is a universally Koszul algebra if, and only if, the graph Γ 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. Minac et al.

Cassella, A., Quadrelli, C. (2021). Right-angled Artin groups and enhanced Koszul properties. JOURNAL OF GROUP THEORY, 24(1), 17-38 [10.1515/jgth-2020-0049].

Right-angled Artin groups and enhanced Koszul properties

Cassella, A
;
Quadrelli, C
2021

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 Γ. Moreover, the same algebra is a universally Koszul algebra if, and only if, the graph Γ 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. Minac et al.
Articolo in rivista - Articolo scientifico
Koszul algebras, Right-angled Artin groups, Galois cohomology,maximal pro-pGalois groups, enhanced Koszul properties, elementary type conjecture.
English
25-ago-2020
2021
24
1
17
38
reserved
Cassella, A., Quadrelli, C. (2021). Right-angled Artin groups and enhanced Koszul properties. JOURNAL OF GROUP THEORY, 24(1), 17-38 [10.1515/jgth-2020-0049].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/282775
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