The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
Bicrossproduct structure of κ-Poincare group and non-commutative geometry
Open accessAbstract
Abstract We show that the κ -deformed Poincare quantum algebra proposed for particle physics has the structure of a Hopf algebra bicrossproduct U(so (1, 3)) T . The algebra is a semidirect product of the classical Lorentz group so (1,3) acting in a formed way on the momentum sector T . The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the κ -Poincare acts covariantly on a κ -Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.
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Cites
Kassel, C. (1994) · Cited by 4,396
q-deformation of Poincaré algebra
Lukierski, J., Ruegg, H., Nowicki, A., & Tolstoy, V. N. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)90358-w · Cited by 820
Self-citationNew quantum Poincaré algebra and κ-deformed field theory
Lukierski, J., Nowicki, A., & Ruegg, H. (1992) · Physics Letters B · doi:10.1016/0370-2693(92)90894-a · Cited by 562
Self-citationMajid, S. (1990) · Journal of Algebra · doi:10.1016/0021-8693(90)90099-a · Cited by 332
Self-citationIntegrable Systems, Quantum Groups, and Quantum Field Theories
(1993) · Springer eBooks · doi:10.1007/978-94-011-1980-1 · Cited by 238
Hopf algebras for physics at the Planck scale
Majid, S. (1988) · Classical and Quantum Gravity · doi:10.1088/0264-9381/5/12/010 · Cited by 223
Self-citationMatched pairs of Lie groups associated to solutions of the Yang-Baxter equations
Majid, S. (1990) · Pacific Journal of Mathematics · doi:10.2140/pjm.1990.141.311 · Cited by 175
Self-citationThree-dimensional quantum groups from contractions of SU(2)q
Celeghini, E., Giachetti, R., Sorace, E., & Tarlini, M. (1990) · Journal of Mathematical Physics · doi:10.1063/1.529000 · Cited by 130
Majid, S. (1991) · Journal of Functional Analysis · doi:10.1016/0022-1236(91)90031-y · Cited by 85
Self-citationExtension theory for connected Hopf algebras
Singer, W. M. (1972) · Journal of Algebra · doi:10.1016/0021-8693(72)90031-2 · Cited by 81
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AMELINO-CAMELIA, G. (2002) · International Journal of Modern Physics D · doi:10.1142/s0218271802001330 · Cited by 1,186
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Hossenfelder, S. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-2 · Cited by 706
Amelino-Camelia, G., & Piran, T. (2001) · Physical Review D · doi:10.1103/physrevd.64.036005 · Cited by 375
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Amelino-Camelia, G., Smolin, L., & Starodubtsev, A. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/13/002 · Cited by 228
Metadata
- Authors
- Majid, S., & Ruegg, H.
- Venue
- Physics Letters B
- Publisher
- Elsevier BV
- Published
- 1994-08
- Volume
- 334
- Issue
- 3-4
- Pages
- 348-354
- ISSN
- 0370-2693 (ISSN-L)
- OpenAlex
- W1992287845
- Cited by
- 799
- References
- 14
- FWCI
- 5.50
- Type
- journal article
- Language
- en
- Open access
- bronze
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