一类商代数上的双-Frobenius代数结构  

Bi-Frobenius Algebraic Structure on a Type of Quotient Algebras

作　　者：王志华 裔小蒙 李金 宣静怡 WANG Zhi-hua;YI Xiao-ineng;LI Jin;XUAN Jing-yi(Department of Mathematical Sciences,Taizhou College,Taizhou 225300,China)

机构地区：[1]泰州学院数理学院

出　　处：《数学的实践与认识》2019年第24期225-230,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11871063);江苏省大学生创新创业训练计划项目(201812917001Z);江苏高校“青蓝工程”资助;江苏省自然科学基金项目(BK20170589)

摘　　要：设C[X]为复数域上的一元多项式代数,I为n+1次Dickson多项式E_(n+1)(X)生成的C[X]的理想,C[X]/I为商代数.证明了商代数C[X]/I既是Frobenius代数,又是Frobenius余代数.进一步,该商代数在恒等对极下还是双-Frobenius代数.Let C[X]be a polynomial algebra with one variable over the field of complex numbers,I the ideal of C[X]generated by the n+1-th Dickson polynomial En+1(X)and C[X]/I the quotient algebra of C[X]modulo the ideal I.It is shown that the quotient algebra C[X]/I is both a Frobenius algebra and a Frobenius coalgebra.Moreover,it is a bi-Frobenius algebra whose antipode is given by the identity map.

关 键 词：FROBENIUS代数 Frobenius余代数 双-Frobenius代数 

分 类 号：O153[理学—数学]