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Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 4, Pages 15–22 (Mi ivm9224)  

Inner derivations of simple Lie pencils of rank $1$

N. A. Koreshkov

Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We prove that simple Lie pencils of rank $1$ over algebraically closed field $P$ of characteristic 0, whose operators of left multiplications have the form of sandwich algebra $M_3(U,\mathcal{D}')$, where $U$ is a subspace of all skew-symmetric matrices in $M_3(P)$, $\mathcal{D}'$ is any subspace containing $\langle E\rangle$ in a space of all diagonal matrices $\mathcal{D}$ in $M_3(P)$.

Keywords: Lie pencil, Cartan subalgebra, torus, inner derivation, sandwich algebra.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:4, 11–17

Bibliographic databases:

UDC: 512.554
Received: 29.09.2015

Citation: N. A. Koreshkov, “Inner derivations of simple Lie pencils of rank $1$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 4, 15–22; Russian Math. (Iz. VUZ), 61:4 (2017), 11–17

Citation in format AMSBIB
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\by N.~A.~Koreshkov
\paper Inner derivations of simple Lie pencils of rank~$1$
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 4
\pages 15--22
\mathnet{http://mi.mathnet.ru/ivm9224}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 4
\pages 11--17
\crossref{https://doi.org/10.3103/S1066369X1704003X}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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