  We construct two quantum spin chains Hamiltonians with quantum sl(2|1)
invariance. These spin chains define variants of the Hubbard model and describe
electron models with pair hoppings. A cubic algebra that admits the
Birman-Wenzl-Murakami algebra as a quotient allows exact solvability of the
periodic chain. The two Hamiltonians, respectively built using the
distinguished and the fermionic bases of U_q(sl(2|1)) differ only in the
boundary terms. They are actually equivalent, but the equivalence is non local.
Reflection equations are solved to get exact solvability on open chains with
non trivial boundary conditions. Two families of diagonal solutions are found.
The centre and the Scasimirs of the quantum enveloping algebra of sl(2|1)
appear as tools for the construction of exactly solvable Hamiltonians.
