The kernel of the determinant map on certain simple C*-algebras

Abstract

Let A be a unital separable simple C*-algebra such that either (1) A has real rank zero, strict comparison and cancellation or (2) A is TAI. We study the kernel of the de la Harpe--Skandalis determinant on GL^0(A), proving that the determinant vanishes exactly on elements which are products of 8 multiplicative commutators. We also have results for the unitary case.

References in corpus (2)

• Homomorphisms from AH-algebras
• Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank One

Cited by in corpus (1)

• Kishimoto's Conjugacy Theorems in simple $C^{\ast }$-algebras of tracial rank one