结合代数Operad的截面理想  

Truncation Ideals of the Associative Algebra Operad

作　　者：魏思凡 王之梁 赵志兵[1] WEI Si-fan;WANG Zhi-liang;ZHAO Zhi-bing(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《合肥学院学报（综合版）》2021年第2期20-26,91,共8页Journal of Hefei University：Comprehensive ED

基　　金：国家自然科学基金项目(11871071);安徽省高校自然科学研究重点项目(KJ2019A0007)资助。

摘　　要：结合代数Operad的理想和多项式恒等代数类有着紧密的联系,其中确定其理想的生成元对于多项式恒等代数的研究有着十分重要的意义。截面理想是结合代数Operad的一类非常重要的理想,而一般的Operad的截面理想的生成元很难计算。通过2-酉Operad的收缩算子和扩张算子构造了新的算子,从而建立了结合代数Operad的不同截面理想之间的联系,并证明了结合代数Operad的第k个截面理想kΥ可由kΥ(k+2)或kΥ(k+1)U k+1Υ(k+2)生成。The ideal of associative algebraic Operad is closely related to the class of polynomial identity algebra,in which the determination of its ideal generator is of great significance to the study of polynomial identity algebra.Truncation ideal is a very important kind of ideal of associative algebraic Operad,but the generator of general truncation ideal is hard to calculate.New operators are constructed by means of restriction operator and extension operator of the 2-unitary Operad,and the connection between different truncation ideals of the associative algebra Operad is established,as well as proved that the k-th truncation ideal of associative algebra Operad kΥcan be generated by kΥ(k+2)or kΥ(k+1)U k+1Υ(k+2).

关 键 词：OPERAD 收缩算子 扩张算子 截面理想 

分 类 号：O152.6[理学—数学]