Abstract :
In this paper we consider the gauge-invariant ideal structure of a C∗-algebra C∗(E,L,B) associated
to a set-finite, receiver set-finite and weakly left-resolving labelled space (E,L,B), where L is a labelling
map assigning an alphabet to each edge of the directed graph E with no sinks. It is obtained that
if an accommodating set B is closed under relative complements, there is a one-to-one correspondence
between the set of all hereditary saturated subsets of B and the gauge-invariant ideals of C∗(E,L,B).
For this, we introduce a quotient labelled space (E,L, [B]R) arising from an equivalence relation ∼R
on B and show the existence of the C∗-algebra C∗(E,L, [B]R) generated by a universal representation
of (E,L, [B]R). Finally we give necessary and sufficient conditions for simplicity of certain labelled graph
C∗-algebras.
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