Geodesic
Inner derivations of simple Lie pencils of rank~$1$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2017), pp. 15-22

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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, inner derivation, sandwich algebra.
Mots-clés : Cartan subalgebra, torus 
@article{IVM_2017_4_a2,
     author = {N. A. Koreshkov},
     title = {Inner derivations of simple {Lie} pencils of rank~$1$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {15--22},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_4_a2/}
}
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N. A. Koreshkov. Inner derivations of simple Lie pencils of rank~$1$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2017), pp. 15-22. http://geodesic.mathdoc.fr/item/IVM_2017_4_a2/