  This paper continues the study of the lower central series quotients of an
associative algebra A, regarded as a Lie algebra, which was started in
math/0610410 by Feigin and Shoikhet. Namely, it provides a basis for the second
quotient in the case when A is the free algebra in n generators (note that the
Hilbert series of this quotient was determined earlier in math/0610410).
Further, it uses this basis to determine the structure of the second quotient
in the case when A is the free algebra modulo the relations saying that the
generators have given nilpotency orders. Finally, it determines the structure
of the third and fourth quotient in the case of 2 generators, confirming an
answer conjectured in math/0610410. Finally, in the appendix, the results of
math/0610410 are generalized to the case when A is an arbitrary associative
algebra (under certain conditions on $A$).
