On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers

  • A. V. Tushev

Abstract

In this paper, we prove the existence of an elementα of the group algebra A=F of a free group F with two generatorsx andy over the field of complex numbers C such that, for any complex a and b for which ¦a¦=¦b¦=1, we have Aϑa,b(α)A=0, where ϑa,b (α is an automorphism of A that maps x,y into ax,by, respectively. Thus, we give a negative answer to question 12.46 of P. A. Linnel from “Kourovka Notebook.”
Published
25.04.1995
How to Cite
Tushev, A. V. “On Ideals of the Group Algebra of a Free Group of Degree of Freedom Two over the Field of Complex Numbers”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 47, no. 4, Apr. 1995, pp. 571-2, https://umj.imath.kiev.ua/index.php/umj/article/view/5460.
Section
Short communications