Differential geometry on linear quantum groups
نویسندگان
چکیده
منابع مشابه
The Differential Calculus on Quantum Linear Groups
The non-commutative differential calculus on the quantum groups SL q (N) is constructed. The quantum external algebra proposed contains the same number of generators as in the classical case. The exterior derivative defined in the constructive way obeys the modified version of the Leibnitz rules.
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The topic of this lecture is differential geometry on quantum groups. Several lecturers at this conference have talked about this subject. For a review and a fairly extensive list of references I would like to point the reader to the contributions of B. Jurco and S. L. Woronowicz in this proceedings. Here we shall propose a new rigid framework for the so-called Cartan calculus of Lie derivative...
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Let A be a cosemisimple Hopf ∗-algebra with antipode S and let Γ be a left-covariant first order differential ∗-calculus over A such that Γ is selfdual (see Section 2) and invariant under the Hopf algebra automorphism S2. A quantum Clifford algebra Cl(Γ, σ, g) is introduced which acts on Woronowicz’ external algebra Γ∧. A minimal left ideal of Cl(Γ, σ, g) which is an A-bimodule is called a spin...
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We outline the recent classification of differential structures for all main classes of quantum groups. We also outline the algebraic notion of ‘quantum manifold’ and ‘quantum Riemannian manifold’ based on quantum group principal bundles, a formulation that works over general unital algebras.
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However, for any point p on the manifold M and for any chart whose domain contains p, there is a convenient basis of the tangent space Tp(M). The third definition is also the most convenient one to define vector fields. A few technical complications arise when M is not a smooth manifold (when k 6=∞), but these are easily overcome using “stationary germs.” As pointed out by Serre in [161] (Chapt...
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 1992
ISSN: 0377-9017,1573-0530
DOI: 10.1007/bf00398310