Anthony Bak (auth.), R. Keith Dennis (eds.)'s Algebraic K-Theory: Proceedings of a Conference Held at PDF

By Anthony Bak (auth.), R. Keith Dennis (eds.)

ISBN-10: 0387119663

ISBN-13: 9780387119663

ISBN-10: 3540119663

ISBN-13: 9783540119661

ISBN-10: 3540395563

ISBN-13: 9783540395560

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Extra resources for Algebraic K-Theory: Proceedings of a Conference Held at Oberwolfach, June 1980 Part II

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Proof. Therefore Bi is a homotopy equivalence. 2. which consists of all objects conjugate to some P c let ~(H,G,H) be the subcategory of (o,eH), o :H + H, R+(H,~), it is easy to see that i maps isomorphically onto a skeleton of ~(H,G,H). right adjoint k to the inclusion, j say, of Let (T,y), T:K ÷ ~ and and all morphisms y = fK E(G/K) H, (l,y). Since o is I1 ~p R+(H,~ ) P ~ It therefore suffices to construct a ~(H,G,H) in C~(G,H) H. be a typical object of k(T,y) = o, where o:H + ~ is specified by o(h) = T(f-lhf).

The group Thus assume If the scalar 2 is non-zero and is not a zero-divisor, then O(n,A) of matrices X c GL(n,A) such that X - I = X t is the group of automorphisms of An which fix the standard quadratic form Q(~ sic i) = ~ a~. could repeat the discussion above with GL(n,A) replaced by O(n,A). However, We it is more appropriate to allow general quadratic forms and, to avoid restrictions concerning 2, to work with bilinear forms rather than quadratic forms. orthogonal A-module, we understand a finite dimensional with a nondegenerate orthogonal symmetric bilinear form.

We single out the orthogonal case. that A is commutative. the group Thus assume If the scalar 2 is non-zero and is not a zero-divisor, then O(n,A) of matrices X c GL(n,A) such that X - I = X t is the group of automorphisms of An which fix the standard quadratic form Q(~ sic i) = ~ a~. could repeat the discussion above with GL(n,A) replaced by O(n,A). However, We it is more appropriate to allow general quadratic forms and, to avoid restrictions concerning 2, to work with bilinear forms rather than quadratic forms.

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Algebraic K-Theory: Proceedings of a Conference Held at Oberwolfach, June 1980 Part II by Anthony Bak (auth.), R. Keith Dennis (eds.)


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