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We give an elementary presentation of the Lie superalgebras, their classification and some properties of their representations. A sketch of the classical Lie supergroup is also given.
We derive a series of stochastic models on linear chains having their stationary probability distributions described by the matrix product Ansatz. We consider models with N different species on a line with closed or open ends. The algebras we obtain and the type of representation depend on the boundary conditions. In the language of quantum chains we obtain the ground state of N-state quantum chains...
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