On quantum Lie algebras and quantum root systems
نویسندگان
چکیده
منابع مشابه
Quantum and Braided Lie Algebras
We introduce the notion of a braided Lie algebra consisting of a finite-dimensional vector space L equipped with a bracket [ , ] : L⊗L → L and a Yang-Baxter operator Ψ : L⊗L → L⊗L obeying some axioms. We show that such an object has an enveloping braided-bialgebra U(L). We show that every generic R-matrix leads to such a braided Lie algebra with [ , ] given by structure constants cK determined ...
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A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions all into one big algebra, the “Cartan Calculus”. (This is an extended versio...
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It is shown that the quantised enveloping algebra of sl(n) contains a quantum Lie algebra, deened by means of axioms similar to Woro-nowicz's. This gives rise to Lie algebra-like generators and relations for the locally nite part of the quantised enveloping algebra, and suggests a canonical Poincar e-Birkhoo-Witt basis.
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The basics of quasitriangular Hopf algebras and quantum Lie algebras are briefly reviewed, and it is shown that their properties allow the introduction of a Killing form. For quantum Lie algebras, this leads to the definitions of a Killing metric and quadratic casimir. The specific case of Uq(su(N)) is examined in detail, where it is shown that many of the classical results are reproduced, and ...
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Quantum groups are born in Leningrad[1] in connection with the quantum inverse problem method as it arises in soliton theory. Other motivations came out after and the logic of the subject has been repeatedly reversed[2] and it is still not univocally established. The approach followed here attempts to use the link of the field with Lie groups as much as it is possible at the moment and, perhaps...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1996
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/29/8/018