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Article overview
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An introduction to non-commutative differential geometry on quantum groups | | P. Aschieri
; L. Castellani
; | | Date: |
26 Jul 1992 | | Journal: | Int.J.Mod.Phys. A8 (1993) 1667-1706 | | Subject: | High Energy Physics - Theory; Quantum Algebra | hep-th math.QA | | Abstract: | We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case ($q
ightarrow 1$ limit). The Lie derivative and the contraction operator on forms and tensor fields are found. A new, explicit form of the Cartan--Maurer equations is presented. The example of a bicovariant differential calculus on the quantum group $GL_q(2)$ is given in detail. The softening of a quantum group is considered, and we introduce $q$-curvatures satisfying q-Bianchi identities, a basic ingredient for the construction of $q$-gravity and $q$-gauge theories. | | Source: | arXiv, hep-th/9207084 | | Services: | Forum | Review | PDF | Favorites | |
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