Presentation of the Iwasawa algebra of the first congruence kernel of a\n semi-simple, simply connected Chevalley group over \ℤ_p

2016/09/11 by Jishnu Ray, Ray, Jishnu · 1 citation
Mathematics · #11R23 #22E35 (Primary) 22E50 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1609.03187

openalex publication_date 2016/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is a general principle that objects coming from semi-simple, simply\nconnected (split) groups have explicit presentations like Serre's presentation\nof semi-simple algebras and Steinberg's presentation of Chevalley groups. In\nthis paper we give an explicit presentation (by generators and relations) of\nthe Iwasawa algebra for the first congruence kernel of a semi-simple, simply\nconnected Chevalley group over \ℤ_p, extending the proof given by\nClozel for the group \Γ₁(SL₂(\ℤ_p)), the first congruence\nkernel of SL₂(\ℤ_p) for primes p>2.\n

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• Presentation of the Iwasawa algebra of the pro-p Iwahori subgroup of\n GL_n(\ℤ_p)

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