Abstract
AbstractLet $$B \subseteq A$$
B
⊆
A
be an inclusion of $$C^*$$
C
∗
-algebras. We study the relationship between the regular ideals of B and regular ideals of A. We show that if $$B \subseteq A$$
B
⊆
A
is a regular $$C^*$$
C
∗
-inclusion and there is a faithful invariant conditional expectation from A onto B, then there is an isomorphism between the lattice of regular ideals of A and invariant regular ideals of B. We study properties of inclusions preserved under quotients by regular ideals. This includes showing that if $$D \subseteq A$$
D
⊆
A
is a Cartan inclusion and J is a regular ideal in A, then $$D/(J\cap D)$$
D
/
(
J
∩
D
)
is a Cartan subalgebra of A/J. We provide a description of regular ideals in the reduced crossed product of a C$$^*$$
∗
-algebra by a discrete group.
Publisher
Springer Science and Business Media LLC
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