Tensor products of coherent configurations

DOI10.1007/S11464-021-0975-9arXiv2105.10679MaRDI QIDQ6368283

Ilya Ponomarenko, Gang Chen

Publication date: 22 May 2021

Abstract: A Cartesian decomposition of a coherent configuration $calX$ is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of $calX$ comes from a certain Cartesian decomposition. It is proved that if the coherent configuration $calX$ is thick, then there is a unique maximal Cartesian decomposition of $calX$, i.e., there is exactly one internal tensor decomposition of $calX$ into indecomposable components. In particular, this implies an analog of the Krull--Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Other designs, configurations (05B30) Graph algorithms (graph-theoretic aspects) (05C85) Products of subgroups of abstract finite groups (20D40) General theory for finite permutation groups (20B05)

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