%0 Journal Article
%T Lie bundle on the space of deformed skew-symmetric matrices
%A Alina Dobrogowska
%A Tomasz Goli¨˝ski
%J Physics
%D 2014
%I arXiv
%R 10.1063/1.4901010
%X 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.
%U http://arxiv.org/abs/1409.8550v1