# Remarks on Quantum Integration

@article{Chryssomalakos1997RemarksOQ, title={Remarks on Quantum Integration }, author={Chryssomalis Chryssomalakos}, journal={Communications in Mathematical Physics}, year={1997}, volume={184}, pages={1-25} }

Abstract: We give a general integration prescription for finite dimensional braided Hopf algebras, deriving the N-dimensional quantum superplane integral as an example. The transformation properties of the integral on the quantum plane are found. We also discuss integration on quantum group modules that lack a Hopf structure.

## 22 Citations

Quantum and Braided Integrals

- Mathematics, Physics
- 1999

We give a pedagogical introduction to integration techniques appropriate for non-commutative spaces. A rather detailed discussion outlines the motivation for adopting the Hopf algebralanguage.…

Invariant integration on classical and quantum Lie supergroups

- Mathematics
- 1999

Invariant integrals on Hopf superalgebras, in particular, the classical and quantum Lie supergroups, are studied. The uniqueness (up to scalar multiples) of a left integral is proved, and a Z2-graded…

Conservation Laws for Linear Equations on Quantum Minkowski Spaces

- Mathematics, Physics
- 1998

Abstract:The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure…

Conservation Laws for Linear Equations on Quantum

- Mathematics
- 1998

The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved cur- rents are given. The proposed procedure can be…

On the braided Fourier transform in the n-dimensional quantum space

- Mathematics
- 1998

We work out in detail a theory of integrability on the braided covector Hopf algebra and the braided vector Hopf algebra of type An introduced by Majid. Using a braided Fourier transform very similar…

Quantum kinematics on q-deformed quantum spaces I, Mathematical Framework

- Physics
- 2006

The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review…

Fourier transform and the Verlinde formula for the quantum double of a finite group

- Mathematics, Physics
- 1999

We define a Fourier transform S for the quantum double D(G) of a finite group G. Acting on characters of D(G), S and the central ribbon element of D(G) generate a unitary matrix representation of the…

Tensor Products of Principal Unitary Representations of Quantum Lorentz Group and Askey-Wilson Polynomials

- Mathematics, Physics
- 1999

We study the tensor product of principal unitary representations of the quantum Lorentz group, prove a decomposition theorem and compute the associated intertwiners. We show that these intertwiners…

Non-relativistic Schroedinger theory on q-deformed quantum spaces I, Mathematical framework and equa

- Mathematics, Physics
- 2007

The aim of these three papers (I, II, and III) is to develop a q-deformed version of non-relativistic Schroedinger theory. Paper I introduces the fundamental mathematical and physical concepts. The…

Integrals of motion for some equations onq-minkowski space

- Physics
- 1997

The conservation laws for second order linear equation with constant coefficients on braided linear space are derived. As an example we study conserved currents connected with symmetry operators for…

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