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2014 | 12 | 6 | 801-812
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Local-global principle for congruence subgroups of Chevalley groups

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Języki publikacji
EN
Abstrakty
EN
Suslin’s local-global principle asserts that if a matrix over a polynomial ring vanishes modulo the independent variable and is locally elementary then it is elementary. In this article we prove Suslin’s local-global principle for principal congruence subgroups of Chevalley groups. This result is a common generalization of the result of Abe for the absolute case and Apte, Chattopadhyay and Rao for classical groups. For the absolute case the localglobal principle was recently obtained by Petrov and Stavrova in the more general settings of isotropic reductive groups.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
6
Strony
801-812
Opis fizyczny
Daty
wydano
2014-06-01
online
2014-03-19
Twórcy
autor
Bibliografia
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  • [6] Basu R., Rao R., Injective stability for K 1 of classical modules, J. Algebra, 2010, 323(4), 867–877 http://dx.doi.org/10.1016/j.jalgebra.2009.12.012
  • [7] Chattopadhyay P., Rao R.A., Elementary symplectic orbits and improved K 1-stability, J. K-Theory, 2011, 7(2), 389–403 http://dx.doi.org/10.1017/is010002021jkt109
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  • [10] Hazrat R., Vavilov N., Zhang Z., Relative unitary commutator calculus, and applications, J. Algebra, 2011, 343, 107–137 http://dx.doi.org/10.1016/j.jalgebra.2011.07.003
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  • [12] Hazrat R., Vavilov N., Zhang Z., Multiple commutator formulas for unitary groups, preprint available at http://arxiv.org/abs/1205.6866v1
  • [13] Hazrat R., Zhang Z., Multiple commutator formulas, Israel J. Math., 2013, 195(1), 481–505 http://dx.doi.org/10.1007/s11856-012-0135-8
  • [14] Jose S., Rao R.A., A local global principle for the elementary unimodular vector group, In: Commutative Algebra and Algebraic Geometry, Contemp. Math., 390, American Mathematical Society, Providence, 2005, 119–125 http://dx.doi.org/10.1090/conm/390/07298
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  • [16] Petrov V.A., Stavrova A.K., Elementary subgroups in isotropic reductive groups, St. Petersburg Math. J., 2009, 20(4), 625–644 http://dx.doi.org/10.1090/S1061-0022-09-01064-4
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  • [19] Stavrova A., Homotopy invariance of non-stable K 1-functors, J. K-Theory (in press), DOI: 10.1017/is013006012jkt232
  • [20] Stepanov A., Vavilov N., On the length of commutators in Chevalley groups, Israel J. Math., 2011, 185, 253–276 http://dx.doi.org/10.1007/s11856-011-0109-2
  • [21] Suslin A.A., On the structure of the special linear group over polynomial rings, Math. USSR-Izv., 1977, 11(2), 221–238 http://dx.doi.org/10.1070/IM1977v011n02ABEH001709
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Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0391-9
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