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Lattices of subrepresentations of Lie algebras and their isomorphisms

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To obtain the representation (L, R) of Lie algebras over the ring Λ, we construct the lattice of subrepresentations ℒ(L, R). Relations between the algebras L and R and the lattice ℒ(L, R) are studied. It turns out that in some cases the isomorphism of the lattice ℒ(L, R) can be continued so as to obtain a wider sublattice ℒ(LλR) consisting of subalgebras of a semidirect product LλR.

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  1. Georgian Technical University, Tbilisi, Georgia

    A. Lashkhi & T. Gelashvili

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  1. A. Lashkhi
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  2. T. Gelashvili
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Correspondence to A. Lashkhi.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 46, Algebra, 2007.

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Lashkhi, A., Gelashvili, T. Lattices of subrepresentations of Lie algebras and their isomorphisms. J Math Sci 153, 518–549 (2008). https://doi.org/10.1007/s10958-008-9135-y

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