Dimension theory and nonstable K1 of quadratic modules

Roozbeh Hazrat

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)

Abstract

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E2n(A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G2n(A, ) G2n0(A, ) G2n1(A, ) E2n(A, ) of the general quadratic group G2n(A, ) such that G2n(A, )/G2n0(A, ) is Abelian, G2n0(A, ) G2n1(A, ) is a descending central series, and G2nd(A)(A, ) = E2n(A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K1,2n(A, ) is solvable when d(A) <.
Original languageEnglish
Pages (from-to)293-328
Number of pages36
JournalK-Theory
Volume27(4)
Issue number4
DOIs
Publication statusPublished - Dec 2002

ASJC Scopus subject areas

  • Mathematics(all)

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