单参数cellular代数的结构  

Structure of Cellular Algebras with a Single Parameter

作　　者：俞海燕 YU Hai-yan(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院

出　　处：《大学数学》2019年第4期15-18,共4页College Mathematics

基　　金：国家自然科学基金(11201449;11471245;16181470)

摘　　要：cellular代数是一种近年来备受关注的代数结构.cellular代数有一个指标集Λ,用以表示这个代数的复杂度.文中研究了单参数cellular代数,即当Λ只包含一个元素时的情形.一般的cellular代数可以看成由这些最简单的cellular代数合成而得.观察到单参数cellular代数作为集合与某个矩阵代数完全相同,但是具有一个由某个对称矩阵决定的乘法.此外还详细研究了对应于各种不同对称矩阵时,相应单参数cellular代数的结构和表示.此外还尝试了在这些代数上构造类似于行列式和迹的函数.Cellular algebra is a algebraic structure received considerable attention in recent years.There is index setΛwhich shows complexity of the corresponding cellular algebra in some sense.We study in detail the so called one parameter cellular algebras whose index setΛcontain only one element.General cellular algebras can be viewed as been composed from one parameter cellular algebras.We observe a one parameter cellular algebra is the same thing with certain matrix algebra as a set,but equipped with a different multiplication rule determined by a symmetric matrix.We study in detail the one parameter cellular algebras corresponding to different symmetric matrices,especially their structure and representations.We also try to construct certain functions on those algebras which could be called determinant and trace.

关 键 词：cellular代数 结合代数 迹 行列式 转置 

分 类 号：O153.3[理学—数学]