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K-Theory of Endomorphism Rings and of Rings of Invariants

✍ Scribed by Martin P Holland

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
269 KB
Volume
191
Category
Article
ISSN
0021-8693

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✦ Synopsis

This paper gives the following description of K of the endomorphism ring of a 0 finitely generated projective module.

THEOREM. Let T be a ring and P a finitely generated, projecti¨e T-module. Let I Ž . Ž . be the trace ideal of P. Then K End P is isomorphic to a subgroup of K T, I . If,

n phic to the subgroup of K T generated by the direct summands of P , for n g ‫.ގ‬ 0 As a corollary we can determine K of the ring of invariants for many free linear 0 actions. In particular, the following result is proved. THEOREM. Let V be a fixed-point-free linear representation of a finite group G o¨er Ž . a field k of characteristic zero and let S V be the symmetric algebra of V. Let K be any Ž Ž . G Ž .. ²w Ž . G Ž .x: finite-dimensional k-¨ector space. Then K S V m S K s S V m S K . 0 k k Ž . Similar results are given for suitable noncommutative versions of S V . ᮊ 1997

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