LIE IDEALS IN TRIDIAGONAL ALGEBRA ALG𝓛∞

• Published : 2015.03.31

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 $T{\in}\mathcal{A}$.

Acknowledgement

Supported by : Daegu University

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Cited by

1. IDEALS IN A TRIDIAGONAL ALGEBRA ALGL∞ vol.34, pp.3_4, 2016, https://doi.org/10.14317/jami.2016.257