关于结合代数的下中心序列
On the lower central series of an associative algebra
摘要：
本文继续了Feigin和Shoikhet在math/0610410中对李代数结合代数A的下中心序列的研究。也就是说，当A是n个生成元中的自由代数时，它为第二个商提供了基础（注意，这个商的希尔伯特级数在前面的数学/0610410中已经确定）。此外，它使用这个基础来确定的情况下，当A是自由代数模的关系说，发电机已给出幂零秩序的第二个商的结构。最后，它确定了在2个生成器的情况下第三和第四个商的结构，证实了math/0610410中给出的答案。最后，在附录中，将math/0610410的结果推广到A是任意结合代数的情况（在$A$上的某些条件下）。
英文摘要：
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 $A$).
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