Tensor products of coherent configurations  

作　　者：Gang CHEN Ilia PONOMARENKO 

机构地区：[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

出　　处：《Frontiers of Mathematics in China》2022年第5期829-852,共24页中国高等学校学术文摘·数学（英文）

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

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.

关 键 词：Coherent configuration Cartesian decomposition Krull-Schmidt theorem 

分 类 号：O15[理学—数学]