Arezoo Aslizadeh, Shahid Beheshti University, Tehran: "The nilpotent multipliers of the direct sum of Lie algebras".
Referent: Arezoo Aslizadeh, Shahid Beheshti University, Tehran
Zeit: Tuesday, 14.02.2019, 17:00h
Ort:Raum 48-436
Abstract: Let L be a Lie algebra presented as the quotient of a free Lie algebra F by an ideal R.
Then the c-nilpotent multiplier of L (c ≥ 1) is de ned to be the abelian Lie algebra M(c)(L) =
R∩γc+1/R,cF. The Lie algebra M(1)(L) = M(L) is more known as the Schur multiplier of L.
Nilpotent multipliers of Lie algebras and their relation to non-abelian tensor products of Lie
algebras were introduced by Salemkar et.al in 2009.
In this talk, I will present an explicit formula for the nilpotent multipliers of the direct sum
of Lie algebras whose abelianisations are nite dimensional and, under some conditions, extend
it for arbitrary Lie algebras. I will also determine the nilpotent multipliers of some certain Lie
algebras and present the exact structure of all c-capable nilpotent Lie algebras with derived
subalgebra of dimension at most 1. This is a joint work with Alireza Salemkar.