Lie bialgebra structures on the extended affine Lie algebra $\widetilde{sl_2(\mathbb{C}_q)}$

Details Lie bialgebra structures on the extended affine Lie algebra $\widetilde{sl_2(\mathbb{C}_q)}$ Lie bialgebra structures on the extended affine Lie algebra $\widetilde{sl_2(\mathbb{C}_q)}$

2011-02-25

arxiv.org/abs/1102.5226v2

Mathematics

Quantum Algebra

19 pages

Scientific paper

Lie bialgebra structures on the extended affine Lie algebra $\widetilde{sl_2(\mathbb{C}_q)}$ are investigated in this paper. Due to the fact that, compared with some classical infinite dimensional graded Lie algebras, there are inner derivations (from itself to its tensor space) which are hidden more deeply in itself's interior algebraic structure, some new techniques need to be employed in order to find them out. It is proved that all Lie bialgebra structures on $\widetilde{sl_2(\mathbb{C}_q)}$ are triangular coboundary.

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