In mathematics and theoretical physics, a superalgebra is a Z2-graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition...

Poisson superalgebra is a Z2-graded generalization of a Poisson algebra. Specifically, a Poisson superalgebra is an (associative) superalgebra A together...

Lie superalgebra is a generalisation of a Lie algebra to include a Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } ‑grading. Lie superalgebras are...

of representation theory, a representation of a Lie superalgebra is an action of Lie superalgebra L on a Z2-graded vector space V, such that if A and...

In mathematics, a supercommutative (associative) algebra is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elements x, y we...

supergraded Lie superalgebra is a further generalization of this notion to the category of superalgebras in which a graded Lie superalgebra is endowed with...

then V is called a vertex operator superalgebra. One of the simplest examples is the vertex operator superalgebra generated by a single free fermion ψ...

Victor G (1977), "Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras", Communications in Algebra, 5 (13): 1375–1400, doi:10...

interesting examples. It is also possible to extend the definition to superalgebras. A generalized Kac–Moody algebra can be graded by giving ei degree 1...

elements f ,   g {\displaystyle f,~g} in V {\displaystyle V} is the obvious superalgebra generalization which unifies CCRs with CARs: if all pure elements are...