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Operator algebra
About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.
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TL;DR: In this article, it was shown that two continuous maps are conjugate if and only if some conjugacy algebra of one is isomorphic to some conjjugacy for the other.
45 citations
TL;DR: A Dirac operator D on quantized irreducible generalized flag manifolds is defined in this article, which yields a Hilbert space realization of the covariant first-order differential calculi constructed by I. Heckenberger and S. Kolb.
Abstract: A Dirac operator D on quantized irreducible generalized flag manifolds is defined. This yields a Hilbert space realization of the covariant first-order differential calculi constructed by I. Heckenberger and S. Kolb. All differentials df=i[D,f] are bounded operators. In the simplest case of Podleś' quantum sphere one obtains the spectral triple found by L. Dabrowski and A. Sitarz.
45 citations
Book•
01 Jan 1991
TL;DR: In this article, the C*-dynamical systems index is used to define bounded derivations, unbounded derivations and uncounted derivations of C* systems.
Abstract: Preface 1. Preliminaries 2. Bounded derivations 3. Unbounded derivations 4. C*-dynamical systems Index.
45 citations
45 citations
TL;DR: In this paper, the authors define the C petertodd*-algebra of quantum real projective space and compute its K-theory, and show that the q-disc of Klimek and Lesniewski can be obtained as a non-Galois Z¯¯¯¯2-quotient of the equator Podleś quantum sphere.
Abstract: We define the C
*-algebra of quantum real projective space R
P
q
2, classify its irreducible representations, and compute its K-theory. We also show that the q-disc of Klimek and Lesniewski can be obtained as a non-Galois Z
2-quotient of the equator Podleś quantum sphere. On the way, we provide the Cartesian coordinates for all Podleś quantum spheres and determine an explicit form of isomorphisms between the C
*-algebras of the equilateral spheres and the C
*-algebra of the equator one.
45 citations