nLab
super Lie algebra

Definition

A super Lie algebra over a field $k$ is a Lie algebra internal to the symmetric monoidal $k$-linear category SVect of super vector spaces.

Examples

• super Poincare Lie algebra

• super q-Schur algebra

Higher generalizations

Just as Lie algebras are categorified to L-infinity algebras and L-infinity algebroids, so super Lie algebras categorifie to super L-infinity algebra?s. A secretly famous example is the

• supergravity Lie 3-algebra

References

One of the original references (or the original reference?) is

• Victor Kac?, Lie superalgebras. Advances in Math. 26 (1977), no. 1, 8–96.

A useful survey with more pointers to the literature is

• L. Frappat, A. Sciarrino, P. Sorba, Dictionary on Lie Superalgebras (arXiv)

Another useful survey is

• D. Leites, Lie superalgebras, J. Soviet Math. 30 (1985), 2481–2512 (web)

• M. Scheunert, The theory of Lie superalgebras. An introduction, Lect. Notes Math. 716 (1979)