TY - JOUR

T1 - Centrality of K_2 for Chevalley groups: a pro-group approach

AU - Лавренов, Андрей Валентинович

AU - Синчук, Сергей Сергеевич

AU - Воронецкий, Егор Юрьевич

PY - 2024/9/1

Y1 - 2024/9/1

N2 - 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.

AB - 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.

UR - https://www.mendeley.com/catalogue/4de03100-e482-3907-a271-76293c297a33/

U2 - 10.1007/s11856-024-2608-y

DO - 10.1007/s11856-024-2608-y

M3 - Article

VL - 262

SP - 97

EP - 142

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

ER -