Covariant (invariant theory)

In algebra, more specifically invariant theory, a covariant of degree k is a homogeneous polynomial map of degree k from the space of binary m-forms to the space of binary p-forms (over the complex numbers) that is $SL_{2}(\mathbb {C} )$-equivariant. A covariant of degree zero is simply an invariant; thus, the notion generalizes the notion of invariant.

There is also a more general ring-theoretic notion of covariants; for that, for now, see module of covariants.

See also

• Invariant of a binary form#Terminology

References

• Claudio Procesi (2007) Lie Groups: an approach through invariants and representation, Springer, ISBN 9780387260402.