Representations of the Cuntz algebra O2 arising from real quadratic transformations
نویسنده
چکیده
We construct representations of the Cuntz algebra O2 from real quadratic transformations of 1-dimensional dynamical systems. By intertwining relations among transformations, we derive relations among operators associated with representations of O2. From these relations, we show properties of these representations.
منابع مشابه
Representations of the Cuntz algebra O3 arising from real cubic transformations
We construct representations of the Cuntz algebra O3 from real cubic transformations on closed intervals. By intertwining relations of transformations, we have those of operators of representations of O2 and O3. By these relations, we show that such representations are unitarily equivalent to barycentric representations.
متن کاملRepresentations of the Cuntz algebra O2 arising from complex quadratic transformations
We study representations of the Cuntz algebra ON arising from dynamical systems with branching(or bifurcation) in [11, 12, 13, 14]. So-called iteration function systems([7]) on dynamical systems are represented as families of isometries on Hilbert spaces so that their composition is corresponded to the product of isometries. In this paper, we treat a representation arising from a naive complex ...
متن کاملComputing the Jones index of quadratic permutation endomorphisms of O 2
We compute the index of the inclusions of type III1/2 factors arising from endomorphisms of the Cuntz algebra O2 associated to the rank-two permutation matrices. MSC 2000: 46L37, 46L05
متن کاملThree representations of the Cuntz algebra O2 by a pair of operators arising from a Z2-graded dynamical system
Representation theory of the Cuntz algebra ON is studied in [1, 2, 4, 5, 6, 8, 9, 10]. Specially, we are interest in a representation of ON arising from a dynamical system (X,F ) which consists of a transformation F on a measure space (X,μ). A class of dynamical systems brings naive and computable examples of representations of ON . A system {fi}i=1 of transformations on X is a branching functi...
متن کاملUniversal fermionization of bosons on permutative representations of the Cuntz algebra O 2
Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. We show a fermionization of bosons which universally holds on any permutative representation of the Cuntz algebra O2. As examples, we show fermionizations on the Fock space and the infinite wedge. Mathematics Subject Classifications (2000). 46K10, 46L60
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003