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Supersymmetry algebras in 1 + 1 dimensions

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A two dimensional Minkowski space, i.e. a flat space with one time and one spacial dimension, has a two-dimensional Poincaré group IO(1,1) as its symmetry group. [1]

12 relations: Central charge, Hermitian matrix, Lie algebra, Lie algebra extension, Lie superalgebra, Lorentz transformation, Minkowski space, Spacetime symmetries, Super-Poincaré algebra, Supercharge, Supersymmetry, Supersymmetry algebra.

Central charge

In theoretical physics, a central charge is an operator Z that commutes with all the other symmetry operators.

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Hermitian matrix

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.

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Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

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Lie algebra extension

In the theory of Lie groups, Lie algebras and their representation theory, a Lie algebra extension is an enlargement of a given Lie algebra by another Lie algebra.

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Lie superalgebra

In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2-grading.

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Lorentz transformation

In physics, the Lorentz transformations (or transformation) are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.

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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

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Spacetime symmetries

Spacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry.

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Super-Poincaré algebra

In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions.

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Supercharge

In theoretical physics, a supercharge is a generator of supersymmetry transformations.

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Supersymmetry

In particle physics, supersymmetry (SUSY) is a theory that proposes a relationship between two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin.

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Supersymmetry algebra

In theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions.

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Redirects here:

N = 1 supersymmetry algebra in 1 + 1 dimensions, N=1 supersymmetry algebra in 1+1 dimensions.

References

[1] https://en.wikipedia.org/wiki/Supersymmetry_algebras_in_1_%2B_1_dimensions

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