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## Derivatives and the role of the Drinfeld twist in Non-commutative string theory,” hepth/0003234

Citations: | 10 - 0 self |

### Citations

772 |
String theory and noncommutative geometry,” JHEP 09
- Seiberg, Witten
- 1999
(Show Context)
Citation Context ...pen strings and Dp-branes with a constant nonvanishing Neveu-Schwarz 2-form Bij have suggested that the noncommutativity which appears is an underlying and very general property of such theories [1]– =-=[14]-=-. Since Hopf algebras (HAs) often lie at the root of noncommutative systems, we were motivated to look for a HA structure for these theories, and showed that the noncommutative ∗-product [15]–[18] was... |

132 | Noncommutative open string and D-brane,” Nucl. Phys. B550 - Chu, Ho - 1999 |

128 |
Moyal, “Quantum mechanics as a statistical theory
- E
- 1949
(Show Context)
Citation Context ...ies [1]– [14]. Since Hopf algebras (HAs) often lie at the root of noncommutative systems, we were motivated to look for a HA structure for these theories, and showed that the noncommutative ∗-product =-=[15]-=-–[18] was in fact a specific case of a more general multiplication defined in terms of the R-matrix R of a quasitriangular HA H; furthermore, when H = F, where F was the HA of functions on R p+1 , as ... |

80 | Noncommutative geometry from 0-branes in a background B-field - Cheung, Krogh - 1998 |

58 | Bialgebra actions, twists, and universal deformation formulas
- Giaquinto, Zhang
- 1998
(Show Context)
Citation Context ...allows us to find a generalisation of the ∗-product and the space of derivations on the algebra constructed with this ∗. (Related but more mathematical treatments of this construction may be found in =-=[21, 22]-=-, and very recently [23], which covers much of the same in a broader context.) However, using the Drinfel’d twist gives exactly the same derivatives and noncommutative product as if we had used an R-m... |

44 | Untwisting noncommutative R g and the equivalence of quantum field theories. Nucl. Phys. B581
- Oeckl
- 2000
(Show Context)
Citation Context ...sation of the ∗-product and the space of derivations on the algebra constructed with this ∗. (Related but more mathematical treatments of this construction may be found in [21, 22], and very recently =-=[23]-=-, which covers much of the same in a broader context.) However, using the Drinfel’d twist gives exactly the same derivatives and noncommutative product as if we had used an R-matrix approach, so why p... |

39 | Towards a Noncommutative Geometric Approach to Matrix Compactification,” Phys. Rev. D58 - Ho, Wu, et al. - 1998 |

28 |
Drinfeld: Quantum groups
- G
- 1986
(Show Context)
Citation Context ...ame, ∆ F = τ ◦ ∆ = ∆ ′ . To compare the antipodes, note that σ −1 becomes m(S ⊗ id)(R21), which is the element, usually denoted u, which generates the square of the antipode in H ∗ : uxu −1 = S 2 (x) =-=[24]-=-. This immediately leads to S F = S −1 = S ′ , exactly as expected, and we see that this choice of F gives (H ∗ ) F = H op , which, as we proved, is the correct choice for the space of derivations on ... |

27 | Noncommutative Geometry and D-Branes - Ho, Wu |

25 | Noncommutative gauge theories - Ho, Wu - 1998 |

22 | Matrix theory on noncommutative torus - Kawano - 1998 |

20 |
Oystaeyen. Quasi-Hopf algebra actions and smash products
- Bulacu, Panaite, et al.
(Show Context)
Citation Context ...allows us to find a generalisation of the ∗-product and the space of derivations on the algebra constructed with this ∗. (Related but more mathematical treatments of this construction may be found in =-=[21, 22]-=-, and very recently [23], which covers much of the same in a broader context.) However, using the Drinfel’d twist gives exactly the same derivatives and noncommutative product as if we had used an R-m... |

13 | Drinfel ′ d. Quasi-Hopf algebras - G - 1990 |

12 | Algebraic Treatment of Compactification on Noncommutative - Casalbuoni - 1998 |

9 | Noncommutative Geometry from - Ardalan, Arfaei, et al. - 1974 |

7 |
Particle Models and Noncommutative
- Connes, Lott
- 1990
(Show Context)
Citation Context ... of open strings and Dp-branes with a constant nonvanishing Neveu-Schwarz 2-form Bij have suggested that the noncommutativity which appears is an underlying and very general property of such theories =-=[1]-=-– [14]. Since Hopf algebras (HAs) often lie at the root of noncommutative systems, we were motivated to look for a HA structure for these theories, and showed that the noncommutative ∗-product [15]–[1... |

7 | Super Yang-Mills on the noncommutative torus - Morariu, Zumino - 1998 |

3 | Noncommutative Geometry and Super-Yang-Mills - Bigatti - 1999 |

2 |
Noncommutative String Theory, the R-Matrix
- Watts
- 2000
(Show Context)
Citation Context ...R of a quasitriangular HA H; furthermore, when H = F, where F was the HA of functions on R p+1 , as was the case for the aforementioned noncommutative string theories, we found an explicit form for R =-=[19]-=- which covers both the commutative (Bij = 0) and noncommutative (Bij ̸= 0) cases. However, it was not immediately apparent how we could introduce derivations on the algebra endowed with this multiplic... |

1 | Fairlie: ‘Moyal Brackets in M-Theory - B - 1998 |

1 |
Fairlie: ‘Moyal Brackets, Star Products and the Generalised Wigner Function
- B
(Show Context)
Citation Context ...1]– [14]. Since Hopf algebras (HAs) often lie at the root of noncommutative systems, we were motivated to look for a HA structure for these theories, and showed that the noncommutative ∗-product [15]–=-=[18]-=- was in fact a specific case of a more general multiplication defined in terms of the R-matrix R of a quasitriangular HA H; furthermore, when H = F, where F was the HA of functions on R p+1 , as was t... |