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EnglishWe construct a 3+-summable spectral triple over the quantum group SUq(2) which is equivariant with respect to a left and a right action of Uq(su(2)). The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.
| Titolo: | The Dirac operator on SUq(2) |
| Autori: | |
| Data di pubblicazione: | 2005 |
| Rivista: | |
| Abstract: | We construct a 3+-summable spectral triple over the quantum group SUq(2) which is equivariant with respect to a left and a right action of Uq(su(2)). The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order. |
| Handle: | http://hdl.handle.net/11368/1695870 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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