Journal of Lie Theory

no. 4
The Lie Superalgebra of a Supermanifold
Journal of Lie Theory, Volume 20 (2010) no. 4, pp. 739-749
We prove a "superversion" of Shanks and Pursell's classical result stating that any isomorphism of the Lie algebras of compactly supported vector fields is implemented by a diffeomorphism of underlying manifolds. We thus provide a Lie algebraic characterization of supermanifolds and describe explicitly isomorphisms of the Lie superalgebras of supervector fields on supermanifolds.
DOI: 10.5802/jolt.617
Classification: 58A50, 17B66, 14F05, 17B70, 17B40
Keywords: Superalgebra, noncommutative space, supermanifold, graded manifold, super vector field, graded Lie algebra 
@article{JOLT_2010_20_4_a6,
     author = {J. Grabowski and A. Kotov and N. Poncin},
     title = {The {Lie} {Superalgebra} of a {Supermanifold}},
     journal = {Journal of Lie Theory},
     pages = {739--749},
     year = {2010},
     volume = {20},
     number = {4},
     doi = {10.5802/jolt.617},
     zbl = {1207.58005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.617/}
}
TY  - JOUR
AU  - J. Grabowski
AU  - A. Kotov
AU  - N. Poncin
TI  - The Lie Superalgebra of a Supermanifold
JO  - Journal of Lie Theory
PY  - 2010
SP  - 739
EP  - 749
VL  - 20
IS  - 4
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.617/
DO  - 10.5802/jolt.617
ID  - JOLT_2010_20_4_a6
ER  - 
%0 Journal Article
%A J. Grabowski
%A A. Kotov
%A N. Poncin
%T The Lie Superalgebra of a Supermanifold
%J Journal of Lie Theory
%D 2010
%P 739-749
%V 20
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.617/
%R 10.5802/jolt.617
%F JOLT_2010_20_4_a6
J. Grabowski; A. Kotov; N. Poncin. The Lie Superalgebra of a Supermanifold. Journal of Lie Theory, Volume 20 (2010) no. 4, pp. 739-749. doi: 10.5802/jolt.617

Cited by Sources: