On the Maximal Containments of Lower Central Series Ideals

2015/09/26 by Rumen Rumenov Dangovski, Dangovski, Rumen Rumenov
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1509.08030

arxiv created 2016/07/07 · arxiv updated 2016/07/08

Abstract

We begin a discussion about the maximal containments of lower central series ideals: ideals generated by products of two-sided ideals of the lower central series of the free associative algebra on n generators. We introduce two new ideas to the topic, the PBW grading and the pigeonhole principle, that help us give a complete classification of the containments for n=2 and obtain partial results in the general case.

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