diff 21e80a8..763cb89 equivariant_jiang_su_stability_v2.txt
diff --git a/equivariant_jiang_su_stability_v2.txt b/equivariant_jiang_su_stability_v2.txt index 8467728..30fa771 100644 --- a/equivariant_jiang_su_stability_v2.txt +++ b/equivariant_jiang_su_stability_v2.txt @@ -12,7 +12,7 @@ a unique tracial state; it is strongly self-absorbing, so $Z \cong Z \otimes Z$. The dimension-drop construction and these properties appear in the study of strongly self-absorbing algebras. -./toms-winter-math0502211-strongly-self-absorbing.pdf +./pdf/toms-winter-math0502211-strongly-self-absorbing.pdf Theorem. Let $A$ be a simple, separable, unital, infinite-dimensional, nuclear, stably finite C*-algebra with $A \cong A \otimes Z$. Let $G$ be a @@ -44,14 +44,14 @@ nonunital case lies outside the present argument. Earlier affirmative cases cover finite algebras with finitely many rays of extremal traces and very weak comparison. -./szabo-1904.10897-equivariant-property-si.pdf +./pdf/szabo-1904.10897-equivariant-property-si.pdf Earlier characterizations of Z-absorption invoke a finiteness restriction on the trace simplex, which the present argument avoids: the Gaussian splittings are uniform over the whole trace space rather than derived from comparison of positive elements. -./matui-sato-1111.1637-strict-comparison-Z-absorption.pdf +./pdf/matui-sato-1111.1637-strict-comparison-Z-absorption.pdf Theorem 1.1 (Matui and Sato). Let $A$ be a unital separable simple infinite-dimensional nuclear C*-algebra with finitely many extremal @@ -66,7 +66,7 @@ an action of a countable amenable group on a separable unital simple nuclear $Z$-stable C*-algebra. Then $\alpha$ has equivariant uniform property Gamma if and only if $\alpha$ is equivariantly Jiang-Su stable. -./szabo-wouters-2301.12846-equivariant-property-gamma.pdf +./pdf/szabo-wouters-2301.12846-equivariant-property-gamma.pdf The forward implication is the absorption step; it remains to construct the required invariant central trace splittings uniformly over the whole @@ -82,7 +82,7 @@ compact convex set, and each trace on the simple algebra $A$ is faithful, because its null space is a closed two-sided ideal not containing the unit. -./haagerup-1403.7653-quasitraces-are-traces.pdf +./pdf/haagerup-1403.7653-quasitraces-are-traces.pdf Theorem 5.11 (Haagerup). Quasitraces on exact unital C*-algebras are traces. Corollary 5.12 (Haagerup). Every stably finite unital exact C*-algebra has a trace state.