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The restricted Weyl group of the Cuntz algebra and shift endomorphisms
-
Roberto Conti
,
Jeong Hee Hong
Published/Copyright:
July 24, 2011
Abstract
It is shown that, modulo the automorphisms which fix the canonical diagonal MASA point-wise, the group of those automorphisms of 𝒪n which globally preserve both the diagonal and the core UHF-subalgebra is isomorphic, via restriction, with the group of those homeomorphisms of the full one-sided n-shift space which eventually commute along with their inverses with the shift transformation. The image of this group in the outer automorphism group of 𝒪n can be embedded into the quotient of the automorphism group of the full two-sided n-shift by its center, generated by the shift. If n is prime then this embedding is an isomorphism.
Received: 2010-06-24
Revised: 2010-12-01
Published Online: 2011-07-24
Published in Print: 2012-06
©[2012] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Diffusion determines the manifold
- Semicomplete meromorphic vector fields on complex surfaces
- Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities
- Almost prime Pythagorean triples in thin orbits
- Hessian inequalities and the fractional Laplacian
- Connected sums of Gorenstein local rings
- The restricted Weyl group of the Cuntz algebra and shift endomorphisms
- Braided cofree Hopf algebras and quantum multi-brace algebras
- Static Klein–Gordon–Maxwell–Proca systems in 4-dimensional closed manifolds
