Geodesic
A Grassmann and Graded Approach to Coboundary Lie Bialgebras, their Classification, and Yang-Baxter Equations
Journal of Lie theory, Tome 30 (2020) no. 4, pp. 1161-1194
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We devise geometric, graded algebra, and Grassmann methods to study and to classify finite-dimensional coboundary Lie bialgebras. Mathematical structures on Lie algebras, like Killing forms, root decompositions, and gradations, are extended to their Grassmann algebras. The classification of real three-dimensional coboundary Lie bialgebras and gl2 up to Lie algebra automorphisms is retrieved throughout devised methods. The structure of modified classical Yang-Baxter equations on so(2,2) and so(3,2) are studied and r-matrices are found.
Classification : 17B62, 17B22, 17B40
Mots-clés : Algebraic Schouten bracket, g-invariant metric, gradation, Grassmann algebra, Lie bialgebra, root decomposition, Killing form 
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     author = {J. de Lucas and D. Wysocki},
     title = {A {Grassmann} and {Graded} {Approach} to {Coboundary} {Lie} {Bialgebras,} their {Classification,} and {Yang-Baxter} {Equations}},
     journal = {Journal of Lie theory},
     pages = {1161--1194},
     year = {2020},
     volume = {30},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2020_30_4_JLT_2020_30_4_a12/}
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J. de Lucas; D. Wysocki. A Grassmann and Graded Approach to Coboundary Lie Bialgebras, their Classification, and Yang-Baxter Equations. Journal of Lie theory, Tome 30 (2020) no. 4, pp. 1161-1194. http://geodesic.mathdoc.fr/item/JLT_2020_30_4_JLT_2020_30_4_a12/