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In the mathematical field 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 B are any two pure elements of L and X and Y are any two pure elements of V, then
Equivalently, a representation of L is a Z2-graded representation of the universal enveloping algebra of L which respects the third equation above.
and 23 Related for: Representation of a Lie superalgebra information
structure ofa graded Lie algebra. Any parabolic Lie algebra is also a graded Lie algebra. A graded Liesuperalgebra extends the notion ofa graded Lie algebra...
the analog ofa universal enveloping algebra ofaLiesuperalgebra which is a unital, associative superalgebra. Let A be asuperalgebra over a commutative...
superalgebra. One of the simplest examples is the vertex operator superalgebra generated by a single free fermion ψ. As a Virasoro representation, it has central...
representation theory of affine Kac–Moody algebras. Liesuperalgebras are generalizations ofLie algebras in which the underlying vector space has a Z2-grading...
theory of SL2(R) Representations of the Lorentz group Stone–von Neumann theorem Unitary representationofa star Liesuperalgebra Zonal spherical function...
is a natural connection between particle physics and representation theory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary...
JSTOR 1968117 Kac, Victor G (1977), "Classification of simple Z-graded Liesuperalgebras and simple Jordan superalgebras", Communications in Algebra, 5 (13): 1375–1400...
is called aLiesuperalgebra. Just as one can have representations ofaLie algebra, one can also have representations ofaLiesuperalgebra, called supermultiplets...
are used in the representation theory ofLie groups and Lie algebras. For example, Verma modules can be constructed as quotients of the universal enveloping...
supergroup of nilpotent length 2. This supergroup has the following Liesuperalgebra. Suppose that M {\displaystyle M} is Minkowski space (of dimension...
are part of a Liesuperalgebra. Let's say we have a quantum system described by a Hamiltonian H {\displaystyle {\mathcal {H}}} and a set of N {\displaystyle...
called aLiesuperalgebra. The simplest supersymmetric extension of the Poincaré algebra is the Super-Poincaré algebra. Expressed in terms of two Weyl...
including Lie 3-algebras and Lie superalgebras. Neither of these fit with Yang–Mills theory. In particular Liesuperalgebras would introduce bosons with...
b} = a0b and a ⋅ b = a−1b. For certain vertex operator algebras, these Poisson algebras are finite-dimensional. Poisson superalgebra Antibracket algebra...
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