Lie ideals in tridiagonal algebra Alg${\mathcal L}_\infty$
Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 351-361
https://doi.org/10.4134/BKMS.2015.52.2.351
Published online March 31, 2015
Joo Ho Kang
Daegu University
Abstract : We give examples of Lie ideals in a tridiagonal algebra Alg${\mathcal L}_\infty$ and study some properties of Lie ideals in Alg${\mathcal L}_\infty$. We also investigate relationships between Lie ideals in Alg${\mathcal L}_\infty$. Let $k$ be a fixed natural number. Let $\mathcal A$ be a linear manifold in Alg${\mathcal L}_\infty$ such that $T_{(2k-1, 2k)} =0$ for all $T \in {\mathcal A}$. Then $\mathcal A$ is a Lie ideal if and only if $T_{(2k-1, 2k-1)} = T_{(2k, 2k)}$ for all $T \in {\mathcal A}$.
Keywords : linear manifold, Lie ideal, tridiagonal algebras
MSC numbers : 47L35
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