Primitivity of unital full free products of finite dimensional C^*-algebras

Details Primitivity of unital full free products of finite dimensional C^*-algebras Primitivity of unital full free products of finite dimensional C^*-algebras

2012-01-23

arxiv.org/abs/1201.4892v1

Mathematics

Operator Algebras

42 pages

Scientific paper

A C^*-algebra is called primitive if it admits a faithful and irreducible
*--representation. We show that the unital C^*-algebra full free product,
A=A_1*A_2, of nontrivial finite dimensional C^*-algebras A_1 and A_2 is
primitive except when A_1 and A_2 are both two dimensional. It follows that A
is antiliminal and the set of pure states is w*-dense in the state space.

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