Some Tits systems with affine Weyl groups in Chevalley groups over Dedekind domains

DOI10.1016/0021-8693(88)90272-4zbMath0685.20036OpenAlexW1963931150MaRDI QIDQ1825963

Jun Morita, Eiichi Abe

Publication date: 1988

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(88)90272-4

zbMATH Keywords

presentationsgroups of unitsaffine Weyl groupDedekind domainChevalley groupIwasawa decompositionTits systemaffine root systemelementary subgroupreduced irreducible root system

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Simple, semisimple, reductive (super)algebras (17B20) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (7)

Groups defined by extended affine Lie algebras with nullity 2 ⋮ Linear groups over general rings. I: Generalities. ⋮ The genetics of universal Chevalley groups over some commutative rings ⋮ Calculations in exceptional groups over rings. ⋮ \(K_ 2\text{SL}_ 2\) of Euclidean domains, generalized Dennis-Stein symbols and a certain three-unit formula ⋮ Symplectic \(K_ 2\) of Laurent polynomials, associated Kac-Moody groups and Witt rings ⋮ Gauss decompositions of kac-moody groups

Cites Work

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• On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups
• Affine root systems and Dedekind's \(\eta\)-function
• Infinite flag varieties and conjugacy theorems
• Generators, Relations and Coverings of Chevalley Groups Over Commutative Rings
• Surjective Stability in Dimension 0 for K 2 and Related Functors

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