Topic
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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01 Jan 1985
169 citations
TL;DR: In this paper, the notions of O∗-algebra and AO∗algebra are defined, which are generalizations of the notion of a C ∗-Algebra and B∗Algebra.
168 citations
TL;DR: In this paper, the deformed Heisenberg algebra (DHA) is used to construct the minimal covariant set of linear differential equations for the fractional spin fields with the help of the deformation of the Klein operator, and a bosonization of supersymmetric quantum mechanics is carried out.
168 citations
TL;DR: In this paper, it was shown that an SL(2,ℝ) conformal symmetry exists if and only if the geometry admits a homothetic Killing vector D a δ a whose associated one-form D a dX a is closed.
Abstract: N-particle quantum mechanics described by a sigma model with an N-dimensional target space with torsion is considered. It is shown that an SL(2,ℝ) conformal symmetry exists if and only if the geometry admits a homothetic Killing vector D a δ a whose associated one-form D a dX a is closed. Further, the SL(2,ℝ) can always be extended to Osp(1|2) superconformal symmetry, with a suitable choice of torsion, by the addition of N real fermions. Extension to SU(1,1|1) requires a complex structure I and a holomorphic U(1) isometry D a I a b δ b . Conditions for extension to the superconformal group D(2,1;α), which involve a triplet of complex structures and SU(2)×SU(2) isometries, are derived. Examples are given.
168 citations
01 Jan 2002
TL;DR: A survey of the theory of finite quantum groupoids (weak Hopf algebras) is given in this article, including foundations and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and 3-manifolds.
Abstract: We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and 3-manifolds.
166 citations