Skip to main content

Injective stability for unitary K1, revisited

  • S. Sinchuk (a1)

We prove the injective stability theorem for unitary K1 under the usual stable range condition on the ground ring. This improves the stability theorem of A. Bak, V. Petrov and G. Tang where a stronger Λ-stable range condition was used.

Hide All
1.Bak, A., K-theory of forms, Ann. Math. Stud. 98, 1981
2.Bak, A., Petrov, V. A., Tang, G., Stability for quadratic K1, K-Theory 30 (1) (2003) 111
3.Bak, A., Tang, G., Stability for Hermitian K1, J. Pure Appl. Algebra 150 (2000) 107121
4.Bak, A., Vavilov, N., Structure of hyperbolic unitary groups. I. Elementary subgroups, Algebra Colloq. 7 (2) (2000) 159196
5.Bass, H., Algebraic K-theory, Benjamin, New York. 1968
6.Hahn, A. J., O'Meara, O. T., The classical groups and K-theory, Springer, Berlin et. al. 1989
7.Hazrat, R., Dimension Theory and Nonstable K1 of Quadratic Modules, K-Theory 27 (2002) 293328
8.Hazrat, R., Vavilov, N., Bak's work on the K-theory of rings, J. K-Theory 4 (1) (2009) 165
9.Knus, M.-A., Quadratic and Hermitian Forms over Rings, Grundl. Math. Wiss. 294, Springer, Berlin, 1991
10.Petrov, V.A., Overgroups of unitary groups, K-Theory 29 (2003) 147174
11.Petrov, V.A., Odd unitary groups, Journal of Math. Sciences 130 (3) (2005) 47524766
12.Plotkin, E., Stein, M. R., Vavilov, N., K1-stability for classical groups revisited. (to appear)
13.Smolensky, A., Sury, B., Vavilov, N., Gauss Decomposition for Chevalley groups, revisited, International Journal of Group Theory 1 (1) (2012) 316
14.Stein, M. R., Stability theorems for K1, K2 and related functors modeled on Chevalley groups, Japan J. Math. 4 (1) (1978) 77108
15.Tang, G., Hermitian Groups and K-Theory, K-Theory 13 (1998) 209267
16.Vaserstein, L. N., Stabilization of unitary and orthogonal groups over a ring, Math. USSR Sbornik 10 (1970) 307326
17.Vaserstein, L. N., You, H., Normal subgroups of classical groups over rings, J. Pure and Applied Algebra 105 (1) (1995) 93105
18.Vavilov, N. A., Sinchuk, S. S., Dennis-Vaserstein type decompositions, Journal of Math. Sciences 171 (3) (2010) 331337
19.Vavilov, N. A., Sinchuk, S. S., Parabolic factorizations of split classical groups, Algebra and Analysis 23 (4) (2011) 131
20.Zhang, Z., Subnormal structure of non-stable unitary groups over rings, J. Pure Appl. Algebra 214 (5) (2010) 622628
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of K-Theory
  • ISSN: 1865-2433
  • EISSN: 1865-5394
  • URL: /core/journals/journal-of-k-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 125 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st March 2018. This data will be updated every 24 hours.