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Glueing operation for R-matrices, quantum groups and link-invariants of Hecke type

Abstract We introduce an associative glueing operation ⊕q on the space of solutions of the Quantum Yang–Baxter Equations of Hecke type. The corresponding glueing operations for the associated quantum groups and quantum vector spaces are also found. The former involves 2×2 quantum matrices whose entries are themselves square or rectangular quantum matrices. The corresponding glueing operation for link-invariants is introduced and involves a state-sum model with Boltzmann weights determined by the link invariants to be glued. The standard su(n) solution, its associated quantum matrix group, quantum space and link-invariant arise at once by repeated glueing of the one-dimensional case.