Dipper-Donkin algebra as global symmetry of quantum chains
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Publication:4947816
DOI10.1088/0305-4470/32/40/308zbMath0962.81029arXivmath/9911034OpenAlexW2074216365MaRDI QIDQ4947816
Publication date: 25 April 2000
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/math/9911034
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Groups and algebras in quantum theory (81R99)
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