Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Cellular filtration of K-theory
and determinants of $C^*$-algebras


Author: Liangqing Li
Journal: Proc. Amer. Math. Soc. 125 (1997), 2637-2642
MSC (1991): Primary 46L80, 46M20, 19K56
DOI: https://doi.org/10.1090/S0002-9939-97-03857-4
MathSciNet review: 1389529
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we will disprove the following conjecture raised by Exel-Loring: Let $A$ be a $C^{*}$-algebra with trace $\tau $ and let $\det : U_{\infty } \to \mathbb {R}/\tau _{*}(K_{0}(A))$ be a determinant associated to $\tau $. If $\phi _{t}: C(S^{3}) \to A ~ (0 \leq t \leq 1)$ is a continuous family of homomorphisms and $b\in C(S^{3})\otimes M_{2}$ is the canonical matrix valued function on $S^{3}$ which represents the Bott element in $K_{1}(C(S^{3}))$, then $\det (\phi _{0}(b)) = \det (\phi _{1}(b))$. It should be noticed that the conjecture has been proved by Exel-Loring for the case that $\phi _{t}$ is a smooth family of homomorphisms.


References [Enhancements On Off] (What's this?)

  • [BBEK] B. Blackadar, O. Bratteli, G. Elliott, and Kumjian, A., Reduction of real rank in inductive limits of $C^{*}$-algebras, Math. Ann. 292 (1992), 111-126. MR 93a:46112
  • [El] G.A. Elliott, On the classification of C*-algebras of real rank zero, J. Reine Angew. Math. 443 (1993), 179-219. MR 94i:46074
  • [EG] G. Elliott and G. Gong, On inductive limits of matrix algebras over two tori, Amer. J. of Math. 118 (1996), 263-290.
  • [EL] G. Elliott and T. Loring, AF embedding of $C(T^{2})$ with prescribed K theory, J. of Functional Analysis 103 (1992), 1-25. MR 93b:46134
  • [Ex] R. Exel, Rotation numbers for automorphisms of $C^{*}$-algebras, Pasific J. of Math 127 (1987), 31-89. MR 88a:46068
  • [ExL] R. Exel and T. Loring, Extending cellular cohomology to, Tran. of AMS 329 (Jan. 1992), 141-160. MR 92e:46137

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L80, 46M20, 19K56

Retrieve articles in all journals with MSC (1991): 46L80, 46M20, 19K56


Additional Information

Liangqing Li
Affiliation: The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1
Address at time of publication: Department of Mathematics, University of Puerto Rico, Rio Piedras, P. O. Box 23355, San Juan, Puerto Rico 00931
Email: li@fields.utoronto.ca

DOI: https://doi.org/10.1090/S0002-9939-97-03857-4
Received by editor(s): January 22, 1996
Received by editor(s) in revised form: March 18, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society