An Upper Bound for the Lower Central Series Quotients of a Free Associative Algebra
نویسندگان
چکیده
منابع مشابه
New Results on the Lower Central Series Quotients of a Free Associative Algebra
We continue the study of the lower central series and its associated graded components for a free associative algebra with n generators, as initiated in [FS]. We establish a linear bound on the degree of tensor field modules appearing in the Jordan-Hölder series of each graded component, which is conjecturally tight. We also bound the leading coefficient of the Hilbert polynomial of each graded...
متن کاملOn the Lower Central Series Quotients of a Graded Associative Algebra
Let A be a noncommutative associative algebra, viewed as a Lie algebra via definition of the Lie bracket [x, y] = xy − yx. Define the lower central series filtration inductively by L1(A) = A, and Li+1(A) = [A,Li(A)]. Denote the components of its associated graded space by Bi(A) = Li(A)/Li+1(A). The components of the associated graded space are well understood in the cases when A = An = the free...
متن کاملLower Central Series of a Free Associative Algebra over the Integers and Finite Fields
Consider the free algebra An generated over Q by n generators x1, . . . , xn. Interesting objects attached to A = An are members of its lower central series, Li = Li(A), defined inductively by L1 = A, Li+1 = [A,Li], and their associated graded components Bi = Bi(A) defined as Bi = Li/Li+1. These quotients Bi for i ≥ 2, as well as the reduced quotient B̄1 = A/(L2 + AL3), exhibit a rich geometric ...
متن کاملA Bound for the Nilpotency Class of a Lie Algebra
In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2008
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnn039