Chevalley groups over commutative rings. I: Elementary calculations

From MaRDI portal
Publication:1815391

DOI10.1007/BF00047884zbMath0861.20044OpenAlexW2171217322MaRDI QIDQ1815391

Eugene Plotkin, Nikolai A. Vavilov

Publication date: 20 May 1997

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00047884



Related Items

Geometry of root elements in groups of type $\mathrm E_{6}$, An explicit presentation of relative Steinberg groups, On the Finiteness length of some soluble linear groups, Decomposition of transvections for automorphisms., Decomposition of transvections: An algebro-geometric approach, An $\mathrm {A}_2$-proof of structure theorems for Chevalley groups of types $\mathrm {E}_6$ and $\mathrm {E}_7$, A generalized Abhyankar's conjecture for simple Lie algebras in characteristic \(p>5\), Cubic forms on adjoint representations of exceptional groups, The commutators of classical groups, \(\mathrm{SL}_2\)-factorizations of Chevalley groups., Linear groups over general rings. I: Generalities., Standardness and standard automorphisms of Chevalley groups. I: The case of rank at least two., On centrality of \(\operatorname{K}_2\) for Chevalley groups of type \(\mathsf{E}_\ell\), The \(R_\infty\)-property for Chevalley groups of types \(B_l\), \(C_l\), \(D_l\) over integral domains., Automorphisms and isomorphisms of Chevalley groups and algebras., Regular bi-interpretability of Chevalley groups over local rings, Bounded generation and commutator width of Chevalley groups: function case, Automorphisms of elementary adjoint Chevalley groups of types \(A_l\), \(D_l\), and \(E_l\) over local rings with \(1/2\)., New and old results on spherical varieties via moduli theory, Relative commutator calculus in Chevalley groups., AN A3-PROOF OF STRUCTURE THEOREMS FOR CHEVALLEY GROUPS OF TYPES E6 AND E7, Automorphisms of Chevalley groups of types \(A_l\), \(D_l\), or \(E_l\) over local rings with \(1/2\)., Calculations in exceptional groups over rings., Chevalley groups of type \(E_7\) in the 56-dimensional representation., Width of groups of type \(\mathrm E_6\) with respect to root elements. II., Orbits of vectors in some representations. I, Uniqueness of representation–theoretic hyperbolic Kac–Moody groups over ℤ, Decomposition of unipotents for \(\mathrm{E}_6\) and \(\mathrm{E}_7\): 25 years after, Elementary equivalence of Chevalley groups over fields., 1-Homotopy of Chevalley Groups, On minimal representations of simple algebraic groups over algebras, ON BI-INVARIANT WORD METRICS, Unitriangular factorizations of Chevalley groups., On the length of commutators in Chevalley groups., Improved stability for the odd-dimensional orthogonal group, Automorphisms of Chevalley groups of type \(F_4\) over local rings with \(1/2\)., The yoga of commutators: further applications., Relative subgroups in Chevalley groups, More variations on the decomposition of transvections., Automorphisms of Chevalley groups of type \(B_l\) over local rings with \(1/2\)., Automorphisms of Chevalley groups of types \(A_l\), \(D_l\), \(E_l\) over local rings without \(1/2\)., Automorphisms of Chevalley groups of different types over commutative rings., Can one see the signs of structure constants?, Decompositions of congruence subgroups of Chevalley groups, Towards the reverse decomposition of unipotents, Chevalley groups of type E7 in the 56-dimensional representation, Classification of all connected subgroup schemes of a reductive group containing a split maximal torus, Generation of relative commutator subgroups in Chevalley groups, Generation of relative commutator subgroups in Chevalley groups. II, Automorphisms of Chevalley groups of types \(B_2\) and \(G_2\) over local rings., Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian, Normalizer of the Chevalley group of type ${\mathrm E}_6$, Weight elements of Chevalley groups, $\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$, Numerology of square equations, Automorphisms of Chevalley groups of type \(G_2\) over local rings without \(1/2\)., Calculations in exceptional groups, an update., Normalizer of the Chevalley group of type ${\operatorname E}_7$, Normal Structure of Maximal Parabolic Subgroups in Chevalley Groups over Rings, Bijective PC-maps of the unipotent radical of the Borel subgroup of the classical symplectic group, Isomorphisms and elementary equivalence of Chevalley groups over commutative rings, A Horrocks-type theorem for even orthogonal \(K_2\), Width of groups of type $\mathrm E_{6}$ with respect to root elements. I, ${\mathrm A}_3$-proof of structure theorems for Chevalley groups of types ${\mathrm E}_6$ and ${\mathrm E}_7$ II. Main lemma, Long root tori in Chevalley groups, Basic reductions in the description of normal subgroups., A third look at weight diagrams, \(K_{1}\) of Chevalley groups are nilpotent



Cites Work