Abstract
We prove the centrality of K2(F4, R) for an arbitrary commutative ring R. This completes the proof of the centrality of K2(Φ, R) for any root system Φ of rank ≥ 3. Our proof uses only elementary localization techniques reformulated in terms of pro-groups. Another new result of the paper is the construction of a crossed module on the canonical homomorphism St(Φ, R) → Gsc(Φ, R), which has not been known previously for exceptional Φ.
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Acknowledgements
The authors of the paper would like to express their sincere gratitude to the anonymous referee for a careful reading of the first version of this paper and numerous helpful suggestions.
The authors of the paper were supported by “Native towns”, a social investment program of PJSC “Gazprom Neft”. The first-named author was also supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No. 075-15-2022-287. The second-named author was also supported by RFBR grant No. 18-31-20044. The second- and third-named authors were also supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”. The first-named author is a winner of Young Russian Mathematics contest and would like to thank its sponsors and the jury.
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Lavrenov, A., Sinchuk, S. & Voronetsky, E. Centrality of K2 for Chevalley groups: a pro-group approach. Isr. J. Math. (2024). https://doi.org/10.1007/s11856-024-2608-y
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DOI: https://doi.org/10.1007/s11856-024-2608-y