  Despite the number of relevant considerations in the literature, the algebra
of generalized symmetries of the Burgers equation has not been exhaustively
described. We fill this gap, presenting a basis of this algebra in an explicit
form and proving that the two well-known recursion operators of the Burgers
equation and two seed generalized symmetries, which are evolution forms of its
Lie symmetries, suffice to generate this algebra. The core of the proof is
essentially simplified by using the original technique of choosing special
coordinates in the associated jet space.
