数学进展
數學進展
수학진전
ADVANCES IN MATHEMATICS
2005年
3期
331-337
,共7页
五边方程%乘法算子%余卷积%Hopf代数
五邊方程%乘法算子%餘捲積%Hopf代數
오변방정%승법산자%여권적%Hopf대수
pentagon equation%multiplicative operator%convolution%Hopf algebra
本文给出五边方程的集合理论解.假设V作用在有限群的张量积G(○)G上,满足五边方程V12V13V23=V23V12,则在给定条件下,V由三元组(a,d,p)惟一确定,其中a,d,p是G到自身的群同态.由此给出了V的分类.
本文給齣五邊方程的集閤理論解.假設V作用在有限群的張量積G(○)G上,滿足五邊方程V12V13V23=V23V12,則在給定條件下,V由三元組(a,d,p)惟一確定,其中a,d,p是G到自身的群同態.由此給齣瞭V的分類.
본문급출오변방정적집합이론해.가설V작용재유한군적장량적G(○)G상,만족오변방정V12V13V23=V23V12,칙재급정조건하,V유삼원조(a,d,p)유일학정,기중a,d,p시G도자신적군동태.유차급출료V적분류.
This paper gives a set-theoretical solution of the pentagon equation. Suppose that there is a map V acting on a finite group G(○)G satisfying the pentagon equation V12V13V23 = V23V12. Then under the given conditions, V is determined uniquely by a triple (a, d, p) where a, d, p are group endomorphisms of G and therefore we give a classfication of V.
