Elements of K1 via the Triple G-construction
نویسنده
چکیده
We represent the elements of K 1 of an exact category by means of two-and three-edge loops in the triple G-construction. The corresponding algebraic data are double short exact sequences and non-commutative 33-diagrams of short exact sequences. We state conjectural relations for the elements of K 1 in terms of 3 3-diagrams. 1. Review of the G-and the triple G-construction In GG] Gillet and Grayson attached a simplicial set G:A to any exact category A and proved that jG:Aj is homotopy equivalent to jQ Aj jS:Aj, the equivalence being natural in A. Thus one can take the formula K m (A) = m (G:A) ; m 0 ; for a deenition of the higher K-groups of A.
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تاریخ انتشار 2007