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Picard Groups of Irrational Rotation C*‐Algebras
Author(s) -
Kodaka Kazunori
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610797005243
Subject(s) - mathematics , automorphism , semidirect product , irrational number , picard group , pure mathematics , group (periodic table) , quadratic equation , section (typography) , rotation (mathematics) , product (mathematics) , combinatorics , algebra over a field , geometry , physics , computer science , quantum mechanics , operating system
Let θ be an irrational number in [0, 1] and A θ the corresponding irrational rotation C*‐algebra. Let Aut ( A θ ) be the group of all automorphisms of A θ and Int ( A θ ) the normal subgroup of Aut ( A θ ) of all inner automorphisms of A θ . Let Pic ( A θ ) be the Picard group of A θ . In the present note we shall show that if θ is not quadratic, then Pic ( A θ )≅Aut ( A θ )/Int ( A θ ) and that if θ is quadratic, then Pic ( A θ ) is isomorphic to a semidirect product of Aut ( A θ )/Int ( A θ ) with Z. Furthermore, in the last section we shall discuss Picard groups of certain Cuntz algebras.