scholarly journals Quantum Lie Algebras and Differential Calculus on Quantum Groups

2013 ◽  
Vol 102 (0) ◽  
pp. 49-66 ◽  
Author(s):  
D. Bernard
Keyword(s):  
Lie Algebras ◽  
Quantum Groups ◽  
Differential Calculus ◽  
Quantum Lie Algebras

scholarly journals Uq(N) GAUGE THEORIES

1994 ◽  
Vol 09 (30) ◽  
pp. 2835-2847 ◽  
Author(s):  
LEONARDO CASTELLANI
Keyword(s):  
Quantum Groups ◽  
Differential Calculus ◽  
Gauge Theories ◽  
Space Time ◽  
Yang Mills ◽  
Commutation Relations ◽  
Transformation Rules ◽  
Field Strengths

Improving on an earlier proposal, we construct the gauge theories of the quantum groups U q(N). We find that these theories are also consistent with an ordinary (commuting) space-time. The bicovariance conditions of the quantum differential calculus are essential in our construction. The gauge potentials and the field strengths are q-commuting "fields," and satisfy q-commutation relations with the gauge parameters. The transformation rules of the potentials generalize the ordinary infinitesimal gauge variations. For particular deformations of U (N) ("minimal deformations"), the algebra of quantum gauge variations is shown to close, provided the gauge parameters satisfy appropriate q-commutations. The q-Lagrangian invariant under the U q(N) variations has the Yang–Mills form [Formula: see text], the "quantum metric" gij being a generalization of the Killing metric.

scholarly journals On quantum Lie algebras and quantum root systems

1996 ◽  
Vol 29 (8) ◽  
pp. 1703-1722 ◽  
Author(s):  
Gustav W Delius ◽  
Andreas Hüffmann
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Quantum Lie Algebras

scholarly journals -Deformed quantum Lie algebras

2006 ◽  
Vol 56 (11) ◽  
pp. 2289-2325 ◽  
Author(s):  
Alexander Schmidt ◽  
Hartmut Wachter
Keyword(s):  
Lie Algebras ◽  
Quantum Lie Algebras
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