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On the maximal finite-dimensional lie algebras with given nilradical

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Abstract

We study the set of finite-dimensional Lie algebras with fixed nilradical (in the capacity of which any nilpotent Lie algebra may serve). We prove an exact estimate for dimensions of Lie algebras from this set. We also show that there may exist several Lie algebras in this set, possessing the maximal dimension. Proofs are based on a concept of algebraic splitting for finite-dimensional Lie algebras.

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References

  1. Snobl, L. “On the structure of Maximal Solvable Wxtensions and of Levi Extensions of Nilpotent Algebras,” J. Phys. A, Math. Theor. 43(505202), 21 (2010).

    MathSciNet  Google Scholar 

  2. Khakimdjanov, Yu. Varieties of Lie Algebra Laws. Handbook of Algebra (Elsevier, 2000), Vol. 2, pp. 509–541.

    MathSciNet  Google Scholar 

  3. Gorbatsevich, V. V. “Splits of Lie groups and their application to the investigation of homogeneous spaces,” Izv. Akad. Nauk SSSR, Ser. Mat. 43, 1227–1258 (1979).

    MATH  MathSciNet  Google Scholar 

  4. Onishchik, A. L., Khakimdzhanov, Yu. B. “On Semidirect Sums of Lie Algebras,” Mat. Zametki 18, 31–40 (1975).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Russian State Technological University, ul. Orshanskaya 3, Moscow, 121552, Russia

    V. V. Gorbatsevich

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  1. V. V. Gorbatsevich
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Correspondence to V. V. Gorbatsevich.

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Original Russian Text © V.V. Gorbatsevich, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 2, pp. 35–44.

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Gorbatsevich, V.V. On the maximal finite-dimensional lie algebras with given nilradical. Russ Math. 59, 29–35 (2015). https://doi.org/10.3103/S1066369X1502005X

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  • DOI: https://doi.org/10.3103/S1066369X1502005X

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