The Dirac operator on compact quantum groups
By Sergey Neshveyev, L. Tuset. 2007
86 citations recorded by the source corpus.
Abstract For the q-deformation Gq , 0 < q < 1, of any simply connected simple compact Lie group G we construct an equivariant spectral triple which is an isospectral deformation of that defined by the Dirac operator D on G. Our quantum Dirac operator Dq is a unitary twist of D considered as an element of U𝔤 ⊗ Cl(𝔤). The commutator of Dq with a regular function on Gq consists of two parts. One is a twist of a classical commutator and so is automatically bounded. The second is expressed in terms of the commutator of the associator with an extension of D. We show that in the case of the Drinfeld associator the latter commutator is also bounded.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4f92766b1cd053d93c21ce11abb678cb09c50084
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Quantized Algebras of Functions on Homogeneous Spaces with Poisson Stabilizers (2011, background): “Later the interest moved more towards noncommutative geometry of these quantum spaces, see for example [6], [7], [21] and references therein, leaving the basic algebraic results scattered in the literature and proved mostly in particular cases with various degrees of generality limited often to SU(2”
- Noncommutative K\"ahler Structures on Quantum Homogeneous Spaces (2011, methodology): “ triples on general Cq[SUN], on the odd and even dimensional quantum spheres, and on all the quantum projective spaces [6, 10, 11, 12, 13]. One of most notable results was that of Neshveyev and Tuset [39], who used a Drinfeld twist to construct spectral triples for all the Drinfeld–Jimbo quantum gro”