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# Supersymmetry algebras in 1 + 1 dimensions

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. 

## Central charge

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

## 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.

## 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.

## 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.

## Lie superalgebra

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

## 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.

## 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.

## Spacetime symmetries

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

## 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.

## Supercharge

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

## 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.

## Supersymmetry algebra

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

## References

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