Symmetry in the Cuntz Algebra on two generators

Abstract

We investigate the structure of the automorphism of ${\mathcal{O}}_2$ which exchanges the two canonical isometries. Our main observation is that the fixed point C*-subalgebra for this action is isomorphic to ${\mathcal{O}}_2$ and we detail the relationship between the crossed-product and fixed point subalgebra.

14 Pages. Minor changes and additions to the references section

References in corpus (1)

• The C*-algebra of symmetric words in two universal unitaries

Cited by in corpus (4)

• A look at the inner structure of the $2$-adic ring $C^{\ast }$-algebra and its automorphism groups
• Normalizers and permutative endomorphisms of the $2$-adic ring $C^{\ast }$-algebra
• On the cyclic automorphism of the Cuntz algebra and its fixed-point algebra
• Yang-Baxter endomorphisms