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...

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...

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

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...

purely algebraically as the universal enveloping algebra of the Lie superalgebra. In a similar way one can define an affine algebraic supergroup as a...

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...

Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra Superconformal algebra Supersymmetry...

called a Lie superalgebra. Just as one can have representations of a Lie algebra, one can also have representations of a Lie superalgebra, called supermultiplets...

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...

spaces. This leads to a treatment of "superobjects" such as superalgebras, Lie superalgebras, supergroups, etc. that is completely analogous to their ungraded...

bilinear map called the Poisson superbracket turning it into a Poisson superalgebra. Every symplectic supermanifold is a Poisson supermanifold but not vice...

supersymmetric quantum mechanics, an application of the supersymmetry superalgebra to quantum mechanics as opposed to quantum field theory. It was hoped...

supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra Lie supergroup Holography Holographic principle AdS/CFT correspondence...

space Feynman integral Poisson algebra Quantum group Renormalization group Representation theory Spacetime algebra Superalgebra Supersymmetry algebra...

In the theory of superalgebras, if A is a commutative superalgebra, V is a free right A-supermodule and T is an endomorphism from V to itself, then the...

applications. The mathematical structure of supersymmetry (graded Lie superalgebras) has subsequently been applied successfully to other topics of physics...

matrix with entries in a superalgebra (or superring). The most important examples are those with entries in a commutative superalgebra (such as a Grassmann...

of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There are two extensions with particular importance in superstring theory:...

Differential graded algebra). A superalgebra is a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded algebra. A graded-commutative superalgebra satisfies the "supercommutative"...

supersymmetry (SUSY) generators form together with the Poincaré algebra a superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes...

therefore may be written as a triple (t, Θ, Θ*). The coordinates form a Lie superalgebra, in which the gradation degree of t is even and that of Θ and Θ* is odd...

Poisson superalgebra and the Gerstenhaber algebra. The difference between the two is in the grading of the product itself. For the Poisson superalgebra, the...

space Feynman integral Poisson algebra Quantum group Renormalization group Representation theory Spacetime algebra Superalgebra Supersymmetry algebra...

algebras (without central charges or internal symmetries), and are Lie superalgebras. Thus a super-Poincaré algebra is a Z2-graded vector space with a graded...

Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra Superconformal algebra Supersymmetry...

The theorem is a generalization of the Coleman–Mandula theorem to Lie superalgebras. It was proved in 1975 by Rudolf Haag, Jan Łopuszański, and Martin Sohnius...