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Outer Automorphisms on Cuntz Algebras
Author(s) -
Matsumoto Kengo,
Tomiyama Jun
Publication year - 1993
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/25.1.64
Subject(s) - mathematics , automorphism , isometry (riemannian geometry) , generator (circuit theory) , pure mathematics , combinatorics , power (physics) , physics , quantum mechanics
We prove that if an automorphism α on the Cuntz algebra O n satisfies α( S 1 ) = ι S 1 for one isometry S 1 of generators S 1 , …, S n such that∑ i = 1 nS i S i * = 1 ,S i * S i = 1 , l ⩽ i ⩽ n and a complex number λ with modulus one, then it is outer. In particular, any non trivial automorphism on O n leaving one generator fixed is outer.