Geodesic
Adjoint Cohomology of Two-Step Nilpotent Lie Superalgebras
Wende Liu1 ; Yong Yang2, 3 ; Xiankun Du2
1School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China
2School of Mathematics, Jilin University, Changchun 130012, P. R. China
3Institute of Physics, University of Pécs, 7622 Hungary
Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 221-232

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

We study the cup products and Betti numbers over cohomology superspaces of two-step nilpotent Lie superalgebras with coefficients in the adjoint modules over an algebraically closed field of characteristic zero. As an application, we prove that the cup product over the adjoint cohomology superspaces for Heisenberg Lie superalgebras is trivial and we also determine the adjoint Betti numbers for Heisenberg Lie superalgebras by means of Hochschild-Serre spectral sequences.
Classification : 17B30, 17B56
Mots-clés : Nilpotent Lie superalgebra, cup product, Betti number, spectral sequence

Wende Liu  1   ; Yong Yang  2 , 3   ; Xiankun Du  2

1 School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China
2 School of Mathematics, Jilin University, Changchun 130012, P. R. China
3 Institute of Physics, University of Pécs, 7622 Hungary 
Wende Liu; Yong Yang; Xiankun Du. Adjoint Cohomology of Two-Step Nilpotent Lie Superalgebras. Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 221-232. http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a10/
@article{JOLT_2021_31_1_a10,
     author = {Wende Liu and Yong Yang and Xiankun Du},
     title = {Adjoint {Cohomology} of {Two-Step} {Nilpotent} {Lie} {Superalgebras}},
     journal = {Journal of Lie Theory},
     pages = {221--232},
     year = {2021},
     volume = {31},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a10/}
}
TY  - JOUR
AU  - Wende Liu
AU  - Yong Yang
AU  - Xiankun Du
TI  - Adjoint Cohomology of Two-Step Nilpotent Lie Superalgebras
JO  - Journal of Lie Theory
PY  - 2021
SP  - 221
EP  - 232
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a10/
ID  - JOLT_2021_31_1_a10
ER  - 
%0 Journal Article
%A Wende Liu
%A Yong Yang
%A Xiankun Du
%T Adjoint Cohomology of Two-Step Nilpotent Lie Superalgebras
%J Journal of Lie Theory
%D 2021
%P 221-232
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a10/
%F JOLT_2021_31_1_a10