1997/06/27 by B. Abdesselam, Abdesselam, Boucif, R. Chakrabarti +1
Chemistry · Engineering · #FOS: Mathematics #Molecular spectroscopy and chirality #Optical Network Technologies #Photonic and Optical Devices #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.q-alg/9706032
openalex publication_date 1997/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the reflection equation algebra for a finite dimensional R-matrix for the (h,w)-deformed Heisenberg algebra \cal Uh,w(h(4)). A representation of the reflection matrix K is constructed using the matrix generators L(±) of the \cal Uh,w(h(4)) algebra. A series of representations of the K-matrix then may be generated by using the coproduct rules of the \cal Uh,w(h(4)) algebra. The complementary condition necessary for combining two distinct solutions of the reflection equation algebra yields the braiding relations between these two sets of generators. This may be thought as a generalization of Bose-Fermi statistics to braiding statistics, which them may be used to provide a new braided colagebraic structure to a Hopf algebra generated by the elements of the matrix K. The reflection equation algebra and the braided exchange properties are found to depend on both deformation parameters h and w.