Stability for Hermitian K1

@article{Bak2000StabilityFH,
  title={Stability for Hermitian K1},
  author={A. Bak and Tang Guoping},
  journal={Journal of Pure and Applied Algebra},
  year={2000},
  volume={150},
  pages={107-121}
}
The general Hermitian group GH2n and its elementary subgroup EH2n are the analogs in the theory of Hermitian forms of the general linear group GLn and its elementary subgroup En. This article proves that the canonical map GH2n/EH2n→GH2(n+1)/EH2(n+1) is an isomorphism whenever n is large with respect to a suitable stable range condition for rings with involution. 
Local-Global Principle for the General Quadratic and General Hermitian Groups and the Nilpotency of KH1
In this article, an analog of the Quillen–Suslin’s local-global principle was established for the elementary subgroup of the general quadratic group and the general Hermitian group. It is shown thatExpand
A note on Quadratic and Hermitian Groups
In this article we deduce an analogue of Quillen's Local-Global Principle for the elementary subgroup of the general quadratic group and the hermitian group. We show that the unstable K_1-groups ofExpand
Stability for odd unitary K1 under the Λ-stable range condition
Abstract Odd unitary groups, introduced by Petrov, generalize and unify all known classical groups. In this paper, the normality of the odd elementary subgroup E U ( V , q ) is re-proved and theExpand
Structure of Hyperbolic Unitary Groups I: Elementary Subgroups
This is the first in a series of papers dedicated to the structure of hyperbolic unitary groups over form rings and their subgroups. In this part, we recall foundations of the theory and study theExpand
Odd Unitary Groups
In the present paper, we introduce a new type of classical-like groups, the so-called odd unitary groups. This notion covers the cases of Bak’s quadratic groups and Hermitian groups. The normality ofExpand
Structure of Hyperbolic Unitary Groups II: Classification of E-normal Subgroups
This paper proves the sandwich classification conjecture for subgroups of an even dimensional hyperbolic unitary group $U_{2n}(R,\Lambda)$ which are normalized by the elementary subgroupExpand
Injective stability for unitary K 1 , revisited
We prove the injective stability theorem for unitary K 1 under the usual stable range condition on the ground ring. This improves the stability theorem of A. Bak, V. Petrov and G. Tang where aExpand
Injective stability for odd unitary K1
Abstract We give a new purely algebraic approach to odd unitary groups using odd form rings. Using these objects, we give a self-contained proof of injective stability for the odd unitaryExpand
Improved K1-stability for the embedding D5 into E6
Abstract This article is dedicated to the surjective stability of the K1-functor for Chevalley groups for the embedding D5 into E6. This case was already studied by Plotkin. In this article, weExpand
Linear groups over general rings. I. Generalities
This paper is the first part of a systematic survey on the structure of classical groups over general rings. We intend to cover various proofs of the main structure theorems, commutator formulas,Expand
...
1
2
3
4
...

References

SHOWING 1-6 OF 6 REFERENCES
The Classical Groups and K-Theory
Notation and Conventions.- 1. General Linear Groups, Steinberg Groups, and K-Groups.- 2. Linear Groups over Division Rings.- 3. Isomorphism Theory for the Linear Groups.- 4. Linear Groups overExpand
Quadratic and Hermitian Forms over Rings
I. Hermitian Forms over Rings.- 1. Rings with Involution.- 2. Sesquilinear and Hermitian Forms.- 3. Hermitian Modules.- 4. Symplectic Spaces.- 5. Unitary Rings and Modules.- 6. Hermitian Spaces overExpand
Absolute stable rank and Witt cancellation for noncommutative rings
Stable range condi t ions on a ring R were devised by H. Bass in order to determine values of n for which every matr ix in GL,(R) can be row reduced (by addi t ion operat ions with coefficients fromExpand
Hermitian Groups and K-Theory
K-Theory of Forms.
Algebraic K-theory