Local properties, bialgebras and representations for one-dimensional tilings
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概要
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For any one-dimensional tiling, we discuss finite dimensional standard modulesfor the associated tiling bialgebra. We will notice that such modules arecompletely reducible, and we will parametrize finite dimensional irreducibleones, using the set of all patches. Furthermore, we will discuss the associatedcompleted groups and Iwasawa-type decompositions. We also characterize forone-dimensional tilings to be locally nondistinguishable by the associated tilingbialgebra structures.
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