On The Solvable Length of Associative Algebras, Matrix Groups, and Lie Algebras

Lie algebras;solvable length

Wood, Lisa M ; Dr. Ernie Stitzinger, Committee Chair,Wood, Lisa M ; Dr. Ernie Stitzinger ; Committee Chair

University:North Carolina State University

关键词: Lie algebras;    solvable length;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/5460/etd.pdf?sequence=2&isAllowed=y

美国|英语

来源: null

【 摘 要 】

Let A be an algebraic system with product a*b between elements a and b in A.It is of interest to compare the solvable length t with other invariants, for instance size, order, or dimension of A.Thus we ask, for a given t what is the smallest n such that there is an A of length t and invariant n.It is this problem that we consider for associative algebras, matrix groups, and Lie algebras.We consider A in each case to be subsets of (strictly) upper triangular n by n matrices.Then the invariant is n.We do these for the associative (Lie) algebras of all strictly upper triangular n by n matrices and for the full n by n upper triangular unipotent groups.The answer for n is the same in all cases.Then we restrict the problem to a fixed number of generators.In particular, using only 3 generators and we get the same results for matrix groups and Lie algebras as for the earlier problem.For associative algebras with 1 generator we also get the same result as the general associative algebra case.Finally we consider Lie algebras with 2 generators and here n is larger than in the general case.We also consider the problem of finding the dimension in the associative algebra, the general, and 3 generator Lie algebra cases.