On the Product of Real Spectral Triples
| dc.creator | Vanhecke, F. J. | |
| dc.date | 1999-02-24 | |
| dc.date | 1999-03-03 | |
| dc.date.accessioned | 2026-07-07T04:32:42Z | |
| dc.date.available | 2026-07-07T04:32:42Z | |
| dc.description | The product of two real spectral triples {A1,H1,D1,J1,gamma1} and {A2,H2,D2,J2(,gamma2)}, the first of which is necessarily even, was defined by A.Connes as {A,H,D,J(,gamma)} given by A=A1 x A2,H=H1 x H2, D=D1 x I2 + gamma1 x D2, J=J1 x J2 and by, in the even-even case, gamma=gamma1 x gamma2. Generically it is assumed that the real structure J obeys the relations J^2=epsilon Id, JD=epsilon' DJ, Jgamma = epsilon'' gammaJ, where the epsilon-sign table depends on the dimension n, modulo 8, of the spectral triple. If both spectral triples obey Connes' epsilon-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this epsilon-sign table. In this note, we propose an alternative definition of the product real structure such that the epsilon-sign table is also satisfied by the product. | |
| dc.description | 8 pages, 5 tables, Latex, Minor misprints in tables 1,3 and 4 corrected | |
| dc.identifier | https://arxiv.org/abs/math-ph/9902029 | |
| dc.identifier | http://arxiv.org/abs/math-ph/9902029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58290 | |
| dc.subject | Mathematical Physics | |
| dc.title | On the Product of Real Spectral Triples | |
| dc.type | text |