St. Petersburg school of linear groups. II: Early works by Suslin

DOI10.1134/s106345412401014xMaRDI QIDQ6638375

Nikolai Vavilov

Publication date: 14 November 2024

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

zbMATH Keywords

algebraic groupsalgebraic \(K\)-theoryclassical groupsChevalley groupslinear groups

Mathematics Subject Classification ID

History of mathematics at specific universities (01A73) Schools of mathematics (01A72) History of group theory (20-03)

Cites Work

• ON THE STRUCTURE OF THE SPECIAL LINEAR GROUP OVER POLYNOMIAL RINGS
• SERRE'S PROBLEM ON PROJECTIVE MODULES OVER POLYNOMIAL RINGS, AND ALGEBRAIC $ K$-THEORY
• LOCALLY POLYNOMIAL RINGS AND SYMMETRIC ALGEBRAS
• ON STABLY FREE MODULES
• On the Normal Subgroups of $G_2(A)$
• Structure of Hyperbolic Unitary Groups I: Elementary Subgroups
• A note on general quadratic groups
• HOMOLOGY OF THE FULL LINEAR GROUP OVER A LOCAL RING, AND MILNOR'SK-THEORY
• THE STEINBERG GROUP OF A POLYNOMIAL RING
• AUTOMORPHISMS OF MATRIX GROUPS OVER COMMUTATIVE RINGS
• Injective stability for unitary K₁, revisited
• The mathematics of Andrei Suslin
• Structure of Hyperbolic Unitary Groups II: Classification of E-Normal Subgroups
• Quillen's solution of Serre's Problem
• Introduction to Algebraic K-Theory. (AM-72)
• ON THE STABILIZATION OF THE GENERAL LINEAR GROUP OVER A RING
• Projective modules over polynomial rings
• Projective modules and complete intersections
• Saint Petersburg school of the theory of linear groups. I: Prehistory
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• Linear groups over general rings. I: Generalities.
• Multiple commutator formulas.
• On centrality of even orthogonal \(\mathrm{K}_2\)
• Dennis-Vaserstein type decompositions.
• Homology stability for linear groups
• Relative unitary commutator calculus, and applications.
• Unitriangular factorizations of Chevalley groups.
• A Horrocks-type theorem for even orthogonal \(K_2\)
• Isomorphisms of a complete linear group over an associative ring
• On centrality of \(\operatorname{K}_2\) for Chevalley groups of type \(\mathsf{E}_\ell\)
• Structure of Chevalley groups over rings via universal localization.
• Odd unitary groups.
• Standard commutator formula.
• Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian
• Algebraic \(K\)-theory and the norm residue homomorphism
• Isomorphisms of unitary groups over associative rings
• Elementary subgroup of a unitary group over a PI-ring
• Homology of \(GL_ n\), characteristic classes and Milnor's K-theory
• Isomorphisms of linear groups over an associative ring
• Algebraic K-theory (in the Steklov mathematical institute of the academy of sciences)
• Location of subgroups in the general linear group over a commutative ring
• On the structure of projective modules over polynomial rings in the case of a noncommutative coefficient ring
• Quadratic modules over polynomial rings
• Schur multiplier of a group of elementary matrices of finite order
• Stabilization theorem for the Milnor \(K_ 2-\)functor
• One theorem of Cohn
• Improvement of \(K_ 2-\)stability under transitive actions of elementary groups
• Quadratic modules and the orthogonal group over polynomial rings
• Nonabelian \(K\)-theory: The nilpotent class of \(K_ 1\) and general stability
• Serre's problem on projective modules over polynomial rings and algebraic K-theory
• A class of projective modules which are nearly free
• Cohomologie et groupe de Steinberg rélatifs
• The relativization of \(K_2\)
• On the stability of the \(K_1\)-functor for Chevalley groups of type \(E_7\)
• Stability for quadratic \(K_1\)
• Stability for Hermitian \(K_1\)
• A local-global principle for symplectic \(\mathrm K_2\)
• Local-global principle for the general quadratic and general Hermitian groups and the nilpotency of \(\mathrm{KH}_1\)
• Standard commutator formula, revisited.
• Dimension theory and nonstable \(K_{1}\) of quadratic modules
• \(K_{1}\) of Chevalley groups are nilpotent
• On homotopy invariance for homology of rank two groups.
• Decomposition of transvections: A theme with variations
• Yoga of commutators in DSER elementary orthogonal group
• An explicit presentation of relative Steinberg groups
• Injective stability for odd unitary \(K_1\)
• Centrality of \(K_2\)-functor revisited
• Local-global principle for congruence subgroups of Chevalley groups.
• The yoga of commutators: further applications.
• The yoga of commutators.
• Algebraic K-theory
• On symplectic groups over polynomial rings
• Chevalley groups of polynomial rings over Dedekind domains
• Injective stability for odd-dimensional unitary \(K_1\)
• Another presentation for symplectic Steinberg groups
• The commutators of classical groups
• Relative commutator calculus in Chevalley groups.
• On the structure of the \(GL_ 2\) of a ring
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Stable rank of rings and dimensionality of topological spaces
• \(K\)-theory and stable algebra
• The Whitehead group of a polynomial extension
• Non-stable \(K_1\)-functors of multiloop groups
• Parabolic factorizations of split classical groups.
• Commutator width in Chevalley groups.
• Lectures on Chevalley Groups
• A Study of Suslin Matrices: Their Properties and Uses
• $ K$-COHOMOLOGY OF SEVERI-BRAUER VARIETIES AND THE NORM RESIDUE HOMOMORPHISM
• THE STABILIZATION OF SYMPLECTIC GROUPS OVER A POLYNOMIAL RING
• Elementary subgroups of isotropic reductive groups
• Bak's work on theK-theory of rings
• Homotopy invariance of non-stable K₁-functors
• The Pillars of Relative Quillen–Suslin Theory
• On a Theorem of Suslin
• Quillen–Suslin theory for classical groups: Revisited over graded rings
• Local-global principle for transvection groups
• A Fundamental Property of Suslin Matrices
• Relative subgroups in Chevalley groups
• Whitehead groups of chevalley groups over polynomial rings
• THE GROUP OF UNITS OF A FREE PRODUCT OF RINGS
• RECIPROCITY LAWS AND THE STABLE RANK OF POLYNOMIAL RINGS
• The general linear group of polynomial rings over regular rings
• ON PROJECTIVE MODULES OVER POLYNOMIAL RINGS
• Skewly computable rows and a theorem of swan and towber

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