Fields and forms on \(\rho\)-algebras. (English) Zbl 1086.58003

Summary: In this paper we introduce noncommutative fields and forms on a new kind of noncommutative algebras: \(\rho\)-algebras. We also define the Frölicher-Nijenhuis bracket in the noncommutative geometry on \(\rho\)-algebras.


58B34 Noncommutative geometry (à la Connes)
46L87 Noncommutative differential geometry
81R60 Noncommutative geometry in quantum theory
16W25 Derivations, actions of Lie algebras
Full Text: DOI arXiv


[1] Bongaarts, P. J M.; Pijls, H. G J., Almost commutative algebra and differential calculus on the quantum hyperplane, J. Math. Phys., 35, 2, 959-970 (1994) · Zbl 0808.17011 · doi:10.1063/1.530888
[2] Cap, A.; Kriegl, A.; Michor, P. W.; Vanzura, J., The Frölicher-Nijenhuis bracket in noncommutative differential geometry, Acta Math. Univ. Comenianae, 62, 1, 17-49 (1993) · Zbl 0830.58002
[3] CiupalĂ, C., Linear connections on almost commutative algebras, Acta Math. Univ. Comenianae, 72, 2, 197-207 (2003) · Zbl 1087.81032
[4] CiupalĂ, C., Connections and distributions on quantum hyperplane, Czech. J. Phys., 54, 8, 821-832 (2004) · doi:10.1023/B:CJOP.0000038590.53753.ef
[5] CiupalĂ, C., ρ-Differential calculi and linear connections on matrix algebra, Int. J. Geom. Methods Mod. Phys., 1, 6, 847-861 (2004) · Zbl 1063.58004 · doi:10.1142/S021988780400040X
[6] Dubois-Violette, M.; Michor, P., More on the Frölicher-Nijenhuis bracket in noncommutative differential geometry, J. Pure Appl. Algebra., 121, 107-135 (1997) · Zbl 0889.58011 · doi:10.1016/S0022-4049(96)00053-9
[7] Lychagin, V., Colour calculus and colour quantizations, Acta Appl. Math., 41, 193-226 (1995) · Zbl 0846.18006 · doi:10.1007/BF00996113
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.