Frontiers of Mathematics in China >

2022 , Vol. 17 >Issue 5: 829 - 852

DOI: https://doi.org/10.1007/s11464-021-0975-9

RESEARCH ARTICLE

Tensor products of coherent configurations

  • Gang CHEN , 1 ,
  • Ilia PONOMARENKO 1,2,3
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  • 1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
  • 2. Steklov Institute of Mathematics at St. Petersburg, Russia
  • 3. Sobolev Institute of Mathematics, Novosibirsk, Russia

Received date: 15 Jul 2021

Accepted date: 16 Aug 2021

Published date: 15 Oct 2022

Copyright

2022 Higher Education Press
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Abstract

A Cartesian decomposition of a coherent configuration ✗ 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 ✗ comes from a certain Cartesian decomposition. It is proved that if the coherent configuration ✗ is thick, then there is a unique maximal Cartesian decomposition of ✗; i.e., there is exactly one internal tensor decomposition of ✗ 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.

Key words： Coherent configuration; Cartesian decomposition; Krull–Schmidt theorem

Cite this article

Gang CHEN , Ilia PONOMARENKO . Tensor products of coherent configurations[J]. Frontiers of Mathematics in China, 2022 , 17(5) : 829 -852 . DOI: 10.1007/s11464-021-0975-9

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