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Nilpotent Lie algebras having the Schur multiplier of maximum dimension. (English) Zbl 1487.17021

P. K. Rai found [Arch. Math. 111, No. 2, 129–133 (2018; Zbl 1448.20020)] a bound for the dimension of the Schur multiplier of a nilpotent Lie algebra in terms of the dimension, n, the nilpotency class, c, and the dimension of the derived algebra, m, to be 1/2(n-m-1)(n+m)-\(\sum_{i=2}^{\min(n-m,c)}\)(n-m-i). In the present work, the authors find all nilpotent Lie algebras whose multiplier meets this bound. For c=2, the algebras are H(1)\(\bigoplus\)A(n-3), L\(_{5,8}\) and L\(_{6,26}\), where the definition of these algebras is given in [“Some results on the Schur multiplier of nilpotent Lie algebras”, Preprint, arXiv:1701.03956] by P. Niroomand and F. Johari. There are no algebras which meet this bound and have c\(>\)2.

MSC:

17B30 Solvable, nilpotent (super)algebras
17B05 Structure theory for Lie algebras and superalgebras
17B99 Lie algebras and Lie superalgebras

Citations:

Zbl 1448.20020
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References:

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