Dipper-Donkin algebra as global symmetry of quantum chains

Details Dipper-Donkin algebra as global symmetry of quantum chains Dipper-Donkin algebra as global symmetry of quantum chains

1999-11-05

arxiv.org/abs/math/9911034v1

J.Phys.A32:7017-7030,1999

Mathematics

Quantum Algebra

30 pages, 3 Figures, LaTex2e

Scientific paper

10.1088/0305-4470/32/40/308

We analize the role of GL_2, a quantum group constructed by Dipper-Donkin, as a global symmetry for quantum chains, and show the way to construct all possible Hamiltonians for four states quantum chains with GL_2 global symmetry. In doing this, we search all inner actions of GL_2 on the Clifford algebra C(1,3) and show them. We also introduce the corresponding operator algebras, invariants and Hamiltonians, explicitly.

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