ISSN:
1573-0514
Keywords:
Transformation groupC *-algebra
;
crossed product
;
Rieffel projection
;
K 0-group
;
homotopy
;
Murray-von Neumann equivalence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetA be the transformation groupC *-algebra associated with an arbitrary orientation-preserving homeomorphism of ℝ. ThisC *-algebra contains an infinite family of projections, called Rieffel projections, each of which generates theK 0-groupK 0(A)≅ℤ. Although these projections must beK-theoretically equivalent, it is easy to see that most are not Murray-von Neumann equivalent. The mystery of how large the matrix algebra must be to implement theK-theory equivalence, is solved by explicitly constructing the equivalence in the smallest possible algebra:A with unit adjoined.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01046940
