On Differential Structures on Quantum Principal Bundles
نویسنده
چکیده
A constructive approach to differential calculus on quantum principal bundles is presented. The calculus on the bundle is built in an intrinsic manner, starting from given graded (differential) *-algebras representing horizontal forms on the bundle and differential forms on the base manifold, together with a family of antiderivations acting on horizontal forms, playing the role of covariant derivatives of regular connections. In this conceptual framework, a natural differential calculus on the structure quantum group is described.
منابع مشابه
General Frame Structures on Quantum Principal Bundles
A noncommutative-geometric generalization of the classical formalism of frame bundles is developed, incorporating into the theory of quantum principal bundles the concept of the Levi-Civita connection. The construction of a natural differential calculus on quantum principal frame bundles is presented, including the construction of the associated differential calculus on the structure group. Gen...
متن کاملNoncommutative Differential Geometry and Twisting of Quantum Groups
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.
متن کاملOn Framed Quantum Principal Bundles
A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type connections are analyzed. A construction of a natural differential calculus on framed bundles is described. Illustrative examples are presented.
متن کاملar X iv : q - a lg / 9 50 70 22 v 1 2 0 Ju l 1 99 5 QUANTUM PRINCIPAL BUNDLES AS HOPF - GALOIS EXTENSIONS
It is shown that every quantum principal bundle with a compact structure group is a Hopf-Galois extension. This property naturally extends to the level of general differential structures, so that every differential calculus over a quantum principal bundle with a compact structure group is a graded-differential variant of the Hopf-Galois extension.
متن کاملLocally trivial quantum vector bundles and associated vector bundles
We define locally trivial quantum vector bundles (QVB) and construct such QVB associated to locally trivial quantum principal fibre bundles. The construction is quite analogous to the classical construction of associated bundles. A covering of such bundles is induced from the covering of the subalgebra of coinvariant elements of the principal bundle. There exists a differential structure on the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994