# On characterizing nilpotent lie algebras by their multipliers

Abstract (Summary)

ATTIOGBE, CYRIL EFOE. On Characterizing Nilpotent Lie algebras by their
Multipliers. (Under the direction of Ernest L. Stitzinger.)
Authors have turned their attentions to special classes of nilpotent Lie
algebras such as two-step nilpotent and filiform Lie algebras, in particular filiform Lie
algebras are classified up to dimension eleven [8]. These techniques have not worked
well in higher dimensions. For a nilpotent Lie algebra L, of dimension n, we consider
central extensions 0MCL0 with M? c2?Z(C), where c2 is the derived algebra of
C and Z(C) is the center of C. Let M(L) be the M of largest dimension and call it the
multiplier of L due to it’s analogy with the Schur multiplier. The maximum dimension
that M can obtain is ½ n(n-1) and this is met if and only if L is abelian.
Let t(L) = ½ n(n-1) - dimM(L). Then t(L) =1 if and only if L=H(1), where H(n) is the
Heisenberg algebra of dimension 2n + 1.
A recent technique to classify nilpotent Lie algebra is to use the dimension of the
multiplier of L. In particular, to find those algebras whose multipliers have dimension
close to the maximum, we call this invariant t(L). Algebras with t(L) ? 8 have been
classified [10]. It’s the purpose of this work to use this technique on filiform Lie algebras
along with three main tools namely: Propositions 0, 3, and theorem 4. All algebras in this
work will be taken over any field whereas in previous works, they have been taken over
the field of real and complex numbers.
Bibliographical Information:

Advisor:

School:North Carolina State University

School Location:USA - North Carolina

Source Type:Master's Thesis

Keywords:north carolina state university

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