
Journal of Lie Theory 30 (2020), No. 4, 11611194 Copyright Heldermann Verlag 2020 A Grassmann and Graded Approach to Coboundary Lie Bialgebras, their Classification, and YangBaxter Equations Javier de Lucas Dept. of Mathematical Methods in Physics, University of Warsaw, 02093 Warsaw, Poland javier.de.lucas@fuw.edu.pl Daniel Wysocki Dept. of Mathematical Methods in Physics, University of Warsaw, 02093 Warsaw, Poland daniel.wysocki@fuw.edu.pl We devise geometric, graded algebra, and Grassmann methods to study and to classify finitedimensional 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 threedimensional coboundary Lie bialgebras and gl_{2} up to Lie algebra automorphisms is retrieved throughout devised methods. The structure of modified classical YangBaxter equations on so(2,2) and so(3,2) are studied and rmatrices are found. Keywords: Algebraic Schouten bracket, ginvariant metric, gradation, Grassmann algebra, Lie bialgebra, root decomposition, Killing form. MSC: 17B62; 17B22, 17B40. [ Fulltextpdf (736 KB)] for subscribers only. 