Journal of Lie Theory 29 (2019), No. 4, 997--1005
Copyright Heldermann Verlag 2019
Some Upper Bounds on the Dimension of the Higher Multiplier of a Pair of Lie Algebras
Mousa Molavi
Department of Pure Mathematics, Shahrekord University, Shahrekord, Iran
mousamolavi@gmail.com
Mohammad Reza Rismanchian
Department of Pure Mathematics, Shahrekord University, Shahrekord, Iran
rismanchian@sku.ac.ir
Mehdi Araskhan
Department of Pure Mathematics, Shahrekord University, Shahrekord, Iran
m.araskhan@iauyazd.ac.ir
We investigate the concept of higher Schur multiplier of a pair of Lie algebras and discuss relevant exact sequences. We will also derive some inequalities between the dimensions of higher Schur multipliers and pairs of their special factor in case of nilpotent Lie algebras. Furthermore, we show new upper bounds for the dimensions.
Keywords: Nilpotent Lie algebras, pair of Lie algebras, c-nilpotent multiplier.
MSC: 17B30, 17B56, 17B99.
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