# American Institute of Mathematical Sciences

March  2017, 9(1): 83-90. doi: 10.3934/jgm.2017003

## The 2-plectic structures induced by the Lie bialgebras

 Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

Received  June 2016 Revised  January 2017 Published  March 2017

In this paper we show that if the Lie algebra $\mathfrak{g}$ admits a Lie bialgebra structure and $\mathcal{D}$ is a Lie group with Lie algebra $\mathfrak{d}$, the double of $\mathfrak{g}$, then $\mathcal{D}$ or its quotient by a suitable Lie subgroup admits a $2$-plectic structure. In particular it is shown that the imaginary part of the Killing form on $\mathfrak{sl}(n, \mathbb{C})$ (as a real Lie algebra) induces a $2$-plectic structure on $SL(n, \mathbb{C})$.

Citation: Mohammad Shafiee. The 2-plectic structures induced by the Lie bialgebras. Journal of Geometric Mechanics, 2017, 9 (1) : 83-90. doi: 10.3934/jgm.2017003
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