# Supergroup (physics)

The concept of supergroup is a generalization of that of group.

[That means every group is a supergroup but not every supergroup is a group.]

First, let's define what a Hopf superalgebra is. Recall that a Hopf algebra is defined category theoretically over the category K-Vect. Similarly, a Hopf superalgebra is defined category theoretically over the category K-Z_2Vect, which is a Z2-graded category. The definitions are the same together with the additional requirement that the morphisms η, [itex]\nabla[itex], ε, Δ and S are all even morphisms.

A Lie supergroup is a supermanifold G together with a morphism [itex]\cdot :G \times G\rightarrow G[itex] which makes G a group object in the category of supermanifolds. This is a generalization of a Lie group.

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