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Holonomy groups and holonomy representations
Journal of Mathematical Physics, 1995The holonomy group of a Riemannian manifold always arises in geometry through a particular representation, not as an abstract group. One can therefore ask whether there exist pairs of (compact, locally irreducible) manifolds with holonomy groups which are isomorphic, yet distinct, because the holonomy representations are not equivalent.
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Extended Holonomy and Topological Invariance of Vanishing Holonomy Group
Journal of Dynamical and Control Systems, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The quantum holonomy associated with a set of contours on a lattice is shown to be a Casimir operator of the gauge group. Its value in an irreducible representation of the group is the unit matrix times a c-number. This assertion is verified numerically on a 4D lattice for the SU(3) pure gauge theory for cases of the set containing one and two ...
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