Differential Calculus on Quantum Spheres

نویسنده

  • Martin Welk
چکیده

We study covariant differential calculus on the quantum spheres S q . A classification result for covariant first order differential ∗ calculi is proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher order calculi and a symmetry concept.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Hermitian metric on quantum spheres

The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.

متن کامل

Quantum and Braided Group Riemannian Geometry

We formulate quantum group Riemannian geometry as a gauge theory of quantum differential forms. We first develop (and slightly generalise) classical Riemannian geometry in a self-dual manner as a principal bundle frame resolution and a dual pair of canonical forms. The role of Levi-Civita connection is naturally generalised to connections with vanishing torsion and cotorsion, which we introduce...

متن کامل

An analytic study on the Euler-Lagrange equation arising in calculus of variations

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

متن کامل

Chiral Fermions on Quantum Four-spheres

We construct wave functions and Dirac operator of spin 1/2 fermions on quantum four-spheres. The construction can be achieved by the q-deformed differential calculus which is manifestly SO(5)q covariant. We evaluate the engenvalue of the Dirac operator on wave functions of the spinors and show that we can define the chiral fermions in such a way that the massless Dirac operator anti-commutes wi...

متن کامل

On the quantum sl2 invariants of knots and integral homology spheres

We will announce some results on the values of quantum sl2 invariants of knots and integral homology spheres. Lawrence’s universal sl2 invariant of knots takes values in a fairly small subalgebra of the center of the h-adic version of the quantized enveloping algebra of sl2 . This implies an integrality result on the colored Jones polynomials of a knot. We define an invariant of integral homolo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1998