See also supersymmetry.
This means that a super Lie algebra is
equipped with a bilinear bracket
that is graded skew-symmetric: is is skew symmetric on and symmetric on .
that satisfied the -graded Jacobi identity:
See the discussion at superalgebra for details on this.
The super Poincare Lie algebra and various of its polyvector extension are super-extension of the ordinary Poincare Lie algebra. These are the supersymmetry algebras in the strict original sense of the word.
higher super Lie algebras
One of the original references (or the original reference?) is
A review of the classification is in
A useful survey with more pointers to the literature is
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)
A useful PhD thesis covering Lie superalgebras and superalgebras more generally is