On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers - Tushev, A. V. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
In this paper, we prove the existence of an elementα of the group algebra A=ℂF 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 A ∩ ϑ_a,b (α)A=0, where ϑ_a,b (α is an automorphism of A that maps x,y into a_x, b_y, respectively. Thus, we give a negative answer to question 12.46 of P. A. Linnel from “Kourovka Notebook.”