We define the second cohomology of a multiplicative Lie algebra K with coefficients in an abelian group H with trivial multiplicative Lie algebra structure in two different cases. Consequently, we prove a natural bijective correspondence between the second cohomology and the set of equivalence classes of some special type of extensions. We also define the notion of Baer sum of extensions for multiplicative Lie algebras.
1
Department of Applied Sciences, Indian Institute of Information Technology, Allahabad, India
Mani Shankar Pandey; Sumit Kumar Upadhyay. Theory of Extensions of Multiplicative Lie Algebras. Journal of Lie Theory, Tome 31 (2021) no. 3, pp. 637-658. http://geodesic.mathdoc.fr/item/JOLT_2021_31_3_a2/
@article{JOLT_2021_31_3_a2,
author = {Mani Shankar Pandey and Sumit Kumar Upadhyay},
title = {Theory of {Extensions} of {Multiplicative} {Lie} {Algebras}},
journal = {Journal of Lie Theory},
pages = {637--658},
year = {2021},
volume = {31},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_3_a2/}
}
TY - JOUR
AU - Mani Shankar Pandey
AU - Sumit Kumar Upadhyay
TI - Theory of Extensions of Multiplicative Lie Algebras
JO - Journal of Lie Theory
PY - 2021
SP - 637
EP - 658
VL - 31
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_3_a2/
ID - JOLT_2021_31_3_a2
ER -
%0 Journal Article
%A Mani Shankar Pandey
%A Sumit Kumar Upadhyay
%T Theory of Extensions of Multiplicative Lie Algebras
%J Journal of Lie Theory
%D 2021
%P 637-658
%V 31
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_3_a2/
%F JOLT_2021_31_3_a2
