五边方程的集合理论解(英文)

On Set-theoretical Solution of the Pentagon Equation

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.

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.