On the Geometry of the Quantum Poincare Group
Paolo Aschieri
TL;DR
This paper explores the geometric structure of the quantum Poincare group, detailing its construction, algebraic properties, and differential calculus, advancing understanding of quantum symmetries in mathematical physics.
Contribution
It introduces a new R-matrix formulation and a bicovariant differential calculus for the quantum Poincare group, expanding the mathematical framework of quantum groups.
Findings
Construction of ISO_qr(N) from SO_qr(N+2)
Development of an R-matrix formulation for U_qr(iso(N))
Establishment of a bicovariant differential calculus on twisted ISO(N)
Abstract
We review the construction of the multiparametric inhomogeneous orthogonal quantum group ISO_qr(N) as a projection from SO_qr(N+2), and recall the conjugation that for N=4 leads to the quantum Poincare group. We study the properties of the universal enveloping algebra U_qr(iso(N)), and give an R-matrix formulation. A quantum Lie algebra and a bicovariant differential calculus on twisted ISO(N) are found.
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