Abstract
According to conclusions made by F. Montaner and E. Zelmanov (unpublished), there exist four Lie bialgebra structures on g[u] up to classical twisting. Therefore we investigated four possible cases for the classical double and the corresponding Lie co-bracket on g[u]. Among them, a new case, where the Lie bialgebra structures are in anone-to-one correspondence with the first introduced herequasi-rational solutions of the CYBE. We also consideredquasi-rational r-matrices in sl(n), particularly, we calculated all the quasi-rationalr-matrices in sl(2).
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Stolin, A., Yermolova-Magnusson, J. The 4th structure. Czech J Phys 56, 1293–1297 (2006). https://doi.org/10.1007/s10582-006-0440-8
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DOI: https://doi.org/10.1007/s10582-006-0440-8