Interrelations between Quantum Groups and Reflection Equation (Braided) Algebras

Abstract

We show that the differential complex ${\Omega }_B$ over the braided matrix algebra $B{M}_q(N)$ represents a covariant comodule with respect to the coaction of the Hopf algebra ${\Omega }_A$ which is a differential extension of $G{L}_q(N)$. On the other hand, the algebra ${\Omega }_A$ is a covariant braided comodule with respect to the coaction of the braided Hopf algebra ${\Omega }_B$. Geometrical aspects of these results are discussed.

8 pages, LaTeX

References in corpus (7)

• Differential Geometry on Linear Quantum Groups
• Quantum and Braided Linear Algebra
• Gauge theories of quantum groups
• Reflection equations and q-Minkowski space algebras
• Quantum Group Gauge Theories and Covariant Quantum Algebras
• GLq(N)-Covariant Quantum Algebras and Covariant Differential Calculus
• GL_q(N)-covariant braided differential bialgebras