Geodesic
A Grassmann and Graded Approach to Coboundary Lie Bialgebras, their Classification, and Yang-Baxter Equations
Javier de Lucas1 ; Daniel Wysocki1
1Dept. of Mathematical Methods in Physics, University of Warsaw, 02-093 Warsaw, Poland
Journal of Lie Theory, Tome 30 (2020) no. 4, pp. 1161-1194

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Javier de Lucas  1   ; Daniel Wysocki  1

1 Dept. of Mathematical Methods in Physics, University of Warsaw, 02-093 Warsaw, Poland 
Javier de Lucas; Daniel 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/JOLT_2020_30_4_a12/
@article{JOLT_2020_30_4_a12,
     author = {Javier de Lucas and Daniel 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/JOLT_2020_30_4_a12/}
}
TY  - JOUR
AU  - Javier de Lucas
AU  - Daniel Wysocki
TI  - A Grassmann and Graded Approach to Coboundary Lie Bialgebras, their Classification, and Yang-Baxter Equations
JO  - Journal of Lie Theory
PY  - 2020
SP  - 1161
EP  - 1194
VL  - 30
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JOLT_2020_30_4_a12/
ID  - JOLT_2020_30_4_a12
ER  - 
%0 Journal Article
%A Javier de Lucas
%A Daniel Wysocki
%T A Grassmann and Graded Approach to Coboundary Lie Bialgebras, their Classification, and Yang-Baxter Equations
%J Journal of Lie Theory
%D 2020
%P 1161-1194
%V 30
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2020_30_4_a12/
%F JOLT_2020_30_4_a12