Symmetry in the Cuntz Algebra on two generators
classification
🧮 math.OA
keywords
fixedmathcalpointsubalgebraactionalgebraautomorphismcanonical
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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.
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