Quantum Lie Algebras and Differential Calculus on Quantum Groups
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概要
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We review the differential calculus on quantum groups following the approach used by Woronowicz. It leads us to introduce two notions of quantum Lie algebras which we refer to as braided or quasi-triangular quantum Lie algebras. They are both different generalizations of the algebras defined by Gurevitch. They are characterized by quadratic relations and braided commutators. The quasi-triangular quantum Lie algebras can be defined as exchange algebras. To any quantum Lie algebra we associate a quantum group with a differential calculus on it such that the algebra of the quantum Lie derivatives is the quantum Lie algebra. We mention two possible `physical' applications: gauge theories on quantum groups and non-local currents in two-dimensional quantum field theories.
- 理論物理学刊行会の論文
- 1991-03-29
著者
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Bernard Denis
Service De Physique Theorique De Saclay : Laboratoire De La Direction Des Sciences De La Matiere Du
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Bernard Denis
Service De Physique Theorique De Saclay : Laboratoire De La Direction Des Sciences De La Matiere Du Commissariat A L'energie Atomique.