Noncommutative analogues of q-special polynomials and q-integral on a quantum sphere
نویسنده
چکیده
The q-Legendre polynomials can be treated as some special ”functions in the quantum double cosets U(1) \ SUq(2)/U(1)”. They form a family (depending on a parameter q) of polynomials in one variable. We get their further generalization by introducing a two parameter family of polynomials. If the former family arises from an algebra which is in a sense ”q-commutative”, the latter one is related to its noncommutative counterpart. We introduce also a two parameter deformation of the invariant integral on a sphere.
منابع مشابه
Noncommutative Balls and Mirror Quantum Spheres
Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the ‘even-dimensional’ case they correspond to the Twisted Canonical Commutation Relations of Pusz and Woronowicz. Then quantum spheres are constructed as double manifolds of noncommutative balls. Both C-algebras and polynomial algebras...
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