Tensor products of coherent configurations

作     者：Gang CHEN Ilia PONOMARENKO Gang CHEN;Ilia PONOMARENKO

作者机构：School of Mathematics and StatisticsCentral China Normal UniversityWuhan 430079China Steklov Institute of Mathematics at St.PetersburgRussia Sobolev Institute of MathematicsNovosibirskRussia 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2022年第17卷第5期

页      面：829-852页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：The first author was supported by the National Natural Science Foundation of China(Grant No.11971189). 

主　　题：Coherent configuration Cartesian decomposition Krull-Schmidt theorem 

摘      要：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.