TY - JOUR
T1 - Regularity of Villadsen algebras and characters on their central sequence algebras
AU - Christensen, Martin S.
PY - 2018
Y1 - 2018
N2 - We show that if A is a simple Villadsen algebra of either the first type with seed space a finite dimensional CW complex, or of the second type, then A absorbs the Jiang-Su algebra tensorially if and only if the central sequence algebra of A does not admit characters. Additionally, in a joint appendix with Joan Bosa (see the following paper), we show that the Villadsen algebra of the second type with infinite stable rank fails the Corona Factorization Property, thus providing the first example of a unital, simple, separable and nuclear C*-algebra with a unique tracial state which fails to have this property.
AB - We show that if A is a simple Villadsen algebra of either the first type with seed space a finite dimensional CW complex, or of the second type, then A absorbs the Jiang-Su algebra tensorially if and only if the central sequence algebra of A does not admit characters. Additionally, in a joint appendix with Joan Bosa (see the following paper), we show that the Villadsen algebra of the second type with infinite stable rank fails the Corona Factorization Property, thus providing the first example of a unital, simple, separable and nuclear C*-algebra with a unique tracial state which fails to have this property.
UR - http://www.scopus.com/inward/record.url?scp=85051065967&partnerID=8YFLogxK
U2 - 10.7146/math.scand.a-104840
DO - 10.7146/math.scand.a-104840
M3 - Journal article
AN - SCOPUS:85051065967
SN - 0025-5521
VL - 123
SP - 121
EP - 141
JO - Mathematica Scandinavica
JF - Mathematica Scandinavica
IS - 1
ER -