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arXiv · 1409.8550

Lie bundle on the space of deformed skew-symmetric matrices

Alina Dobrogowska·Tomasz Goliński
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Abstract

We study a Lie algebra $\mathcal A_{a_1,\ldots,a_{n-1}}$ of deformed skew-symmetric $n \times n$ matrices endowed with a Lie bracket given by a choice of deformed symmetric matrix. The deformations are parametrized by a sequence of real numbers $a_1,\ldots,a_{n-1}$. Using isomorphism $\mathcal A_{a_1,\ldots,a_{n-1}}^* \cong L_+$ we introduce a Lie-Poisson structure on the space of upper-triangular matrices $L_+$. In this way we generate hierarchies of Hamilton systems with bihamiltonian structure.

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Alina Dobrogowska, Tomasz Goliński. 2014-09-30. Lie bundle on the space of deformed skew-symmetric matrices. https://doi.org/10.1063/1.4901010

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