An introduction to non-commutative differential geometry on quantum groups

Journal Article · Tue Apr 20 00:00:00 EDT 1993 · International Journal of Modern Physics A; (United States)

OSTI ID:5918845

Aschieri, P ^[1]; Castellani, L ^[2]

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1. CERN, Geneva (Switzerland)
2. Inst. Nazionale di Fisica Nucleare, Torino (Italy)

The authors give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case (q [yields] 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[sub q](2) is given in detail. The softening of a quantum group is considered, and they introduce q-curvatures satisfying q-Bianchi identifies, a basic ingredient for the construction of q-gravity and q-gauge theories.

• OSTI ID: 5918845
• Journal Information: International Journal of Modern Physics A; (United States), Vol. 8:10; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
LIE GROUPS
DIFFERENTIAL CALCULUS
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QUANTUM GRAVITY
SYMMETRY BREAKING
TENSOR FIELDS
UNIFIED GAUGE MODELS
FIELD THEORIES
MATHEMATICAL MODELS
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PARTICLE MODELS
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SYMMETRY GROUPS
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