Proceedings ArticleDOI
Equivariant spectral triples
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In this paper, the authors introduce the notion of equivariant spectral triples with Hopf algebras as isometries of non-commutative manifolds.Abstract:
We present the review of noncommutative symmetries applied to Connes’ formulation of spectral triples. We introduce the notion of equivariant spectral triples with Hopf algebras as isometries of noncommutative manifolds, relate it to other elements of theory (equivariant K-theory, homology, equivariant differential algebras) and provide several examples of spectral triples with their isometries: isospectral (twisted) deformations (including noncommutative torus) and finite spectral triples.read more
Citations
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Journal ArticleDOI
The Dirac Operator on SU q (2)
TL;DR: In this article, a 3+summable spectral triple Open Image in new window over the quantum group SUq(2) which is equivariant with respect to a left and a right action was constructed.
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The Dirac operator on SU_q(2)
TL;DR: In this paper, a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q (2) which is equivariant with respect to a left and a right action was constructed.
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Dirac Operators on Quantum Projective Spaces
TL;DR: In this paper, a family of self-adjoint operators D-N with compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CPql, for any l >= 2 and 0 < q < 1.
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Dirac operators on all Podles quantum spheres
TL;DR: In this paper, the authors construct spectral triples on all Podles quantum spheres S 2 qt, which are equivariant for a left action of Uq(su(2)) and are regular, even and of metric dimension 2.
Posted Content
Equivariant Poincar\'e duality for quantum group actions
Ryszard Nest,Christian Voigt +1 more
TL;DR: In this paper, the notion of Poincar´e duality in KK-theory was extended to the setting of quantum group actions, and an important ingredient in this approach is the replacement of ordinary tensor products by braided tensor product.
References
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Vyjayanthi Chari,Andrew Pressley +1 more
TL;DR: In this paper, the Kac-Moody algebras and quasitriangular Hopf algesas were used to represent the universal R-matrix and the root of unity case.
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TL;DR: In this paper, the authors define Hopf algebras as "quasitriangular Hopf-algebraes" and introduce matrix quantum groups and bicrossproduct hopf alges.
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TL;DR: In this article, the authors present a general overview of Banach Algebras and C*-AlgebrAs, as well as a discussion of their properties and properties.