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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 4, Pages 15–22
(Mi ivm9224)
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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.
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
Linking options:
https://www.mathnet.ru/eng/ivm9224 https://www.mathnet.ru/eng/ivm/y2017/i4/p15
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Abstract page: | 106 | Full-text PDF : | 23 | References: | 25 | First page: | 6 |
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