On the filtration of a free algebra by its associative lower central series
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 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 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...
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the aim of this thesis is an approach for assessing insurer’s solvency for iranian insurance companies. we use of economic data with both time series and cross-sectional variation, thus by using the panel data model will survey the insurer solvency.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2013
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.10.032