La K-Théorie de la C*-Algèbre Pleine de SL3(C)

✍ Scribed by Francois Pierrot

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 189 KB
• Volume: 193
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2001.3907

✦ Synopsis

Let G be SL 3 ðCÞ, l : C * ðGÞ ! C * r ðGÞ the morphism induced by the regular representation, and e : C * ðGÞ ! C the trivial representation. We prove that l È e induces a KK-equivalence between C * ðGÞ and C * r ðGÞ È C. We prove this by comparing C * ðGÞ with CðG=PÞsG where P is a maximal parabolic subgroup in G. As a corollary, we obtain the computation of K * ðC * ðGÞÞ. # 2002 Elsevier Science (USA) * On a K 1 ðC * ðSL 3 ðCÞÞÞ ¼ 0.