Yoga of commutators in DSER elementary orthogonal group

DOI10.1007/s40062-018-0223-5zbMath1473.19005OpenAlexW2964103957WikidataQ128988342 ScholiaQ128988342MaRDI QIDQ2002828

A. A. Ambily

Publication date: 12 July 2019

Published in: Journal of Homotopy and Related Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40062-018-0223-5

zbMATH Keywords

orthogonal grouplocal-global principlequadratic modulesDickson-Siegel-Eichler-Roy transformations

Mathematics Subject Classification ID

(K)-theory of quadratic and Hermitian forms (11E70) Projective and free modules and ideals in commutative rings (13C10) Other matrix groups over rings (20H25) (K)-theory of forms (19G99)

Related Items (4)

Comparison of Petrov’s odd elementary hyperbolic unitary group and Dickson-Siegel-Eichler-Roy elementary orthogonal group ⋮ Normality and \(K_1\)-stability of Roy's elementary orthogonal group ⋮ Normality of DSER elementary orthogonal group ⋮ Homotopy and commutativity principle

Uses Software

• GAP

Cites Work

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• Multiple commutator formulas.
• Equality of linear and symplectic orbits
• Structure of Chevalley groups over rings via universal localization.
• Nonabelian \(K\)-theory: The nilpotent class of \(K_ 1\) and general stability
• Linear relations in Eichler orthogonal transformations
• Hermitian groups and \(K\)-theory
• Dimension theory and nonstable \(K_{1}\) of quadratic modules
• Generating modules efficiently: Theorems from algebraic K-theory
• \(K_{1}\) of Chevalley groups are nilpotent
• Local-global principle for congruence subgroups of Chevalley groups.
• The yoga of commutators.
• Normality of DSER elementary orthogonal group
• Extendability of quadratic modules over a polynomial extension of an equicharacteristic regular local ring
• Normality and \(K_1\)-stability of Roy's elementary orthogonal group
• Cancellation of quadrate forms over commutative rings
• Bak's work on theK-theory of rings
• Cancellation of quadratic forms over polynomial rings
• An Elementary Transformation of a Special Unimodular Vector to Its Top Coefficient Vector
• Local-global principle for transvection groups
• Structure of Hyperbolic Unitary Groups II: Classification of E-Normal Subgroups
• Nilpotency of Odd Unitary K₁-Functor
• Projective modules over polynomial rings

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