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<p>In this paper, we study the stabilization map on the relative <i>Dickson-Siegel-Eichler-Roy</i> (DSER) elementary orthogonal group. We obtain two bounds for the hyperbolic rank of the underlying quadratic space such that the stabilization map on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textrm{K}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>K</mtext> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>- analogue of the relative <i>DSER</i> elementary orthogonal group becomes an isomorphism and a monomorphism.</p>

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On \(\textrm{K}_1\)-stability of the relative DSER elementary orthogonal group

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • A. A. Ambily,
  • Gayathry Pradeep

摘要

In this paper, we study the stabilization map on the relative Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal group. We obtain two bounds for the hyperbolic rank of the underlying quadratic space such that the stabilization map on \(\textrm{K}_1\) K 1 - analogue of the relative DSER elementary orthogonal group becomes an isomorphism and a monomorphism.