# Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces

## Abstract

We study the general deformed conformal-Poincare (Galilean) symmetries consistent with relativistic (nonrelativistic) canonical noncommutative spaces. In either case we obtain deformed generators, containing arbitrary free parameters, which close to yield new algebraic structures. We show that a particular choice of these parameters reproduces the undeformed algebra. The modified coproduct rules and the associated Hopf algebra are also obtained. Finally, we show that for the choice of parameters leading to the undeformed algebra, the deformations are represented by twist functions.

- Authors:

- S.N. Bose National Centre for Basic Sciences, JD Block, Sector 3, Salt Lake, Kolkata 700098 (India)
- (India)

- Publication Date:

- OSTI Identifier:
- 21011101

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.045008; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; COMMUTATION RELATIONS; CONFORMAL INVARIANCE; QUANTUM FIELD THEORY; RELATIVISTIC RANGE; SYMMETRY

### Citation Formats

```
Banerjee, Rabin, Kumar, Kuldeep, and Department of Physics, Panjab University, Chandigarh 160014.
```*Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.045008.

```
Banerjee, Rabin, Kumar, Kuldeep, & Department of Physics, Panjab University, Chandigarh 160014.
```*Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces*. United States. doi:10.1103/PHYSREVD.75.045008.

```
Banerjee, Rabin, Kumar, Kuldeep, and Department of Physics, Panjab University, Chandigarh 160014. Thu .
"Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces". United States.
doi:10.1103/PHYSREVD.75.045008.
```

```
@article{osti_21011101,
```

title = {Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces},

author = {Banerjee, Rabin and Kumar, Kuldeep and Department of Physics, Panjab University, Chandigarh 160014},

abstractNote = {We study the general deformed conformal-Poincare (Galilean) symmetries consistent with relativistic (nonrelativistic) canonical noncommutative spaces. In either case we obtain deformed generators, containing arbitrary free parameters, which close to yield new algebraic structures. We show that a particular choice of these parameters reproduces the undeformed algebra. The modified coproduct rules and the associated Hopf algebra are also obtained. Finally, we show that for the choice of parameters leading to the undeformed algebra, the deformations are represented by twist functions.},

doi = {10.1103/PHYSREVD.75.045008},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

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