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On the classification of Lagrangian subalgebras in $\mathfrak{g}\times\mathfrak{g}$, where $\mathfrak{g}$ is a complex reductive Lie algebra

E. A. Karolinsky

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov

Abstract: An inductive approach to the classification of Lagrangian subalgebras in $\mathfrak{g}\times\mathfrak{g}$ up to the diagonal $\operatorname{Int}\mathfrak{g}$-action is proposed. Using this approach, the classification of Lagrangian subalgebras in $\mathfrak{g}\times\mathfrak{g}$, where $\mathfrak{g}=sl(n)$, $n\leq4$, is obtained.

Received: 18.12.1996