Given a Hopf algebra and a right -comodule (where is a right coaction), a subspace is coinvariant subspace foir coaction if . If is a -comodule algebra, viewed as a (formal dual to) noncommutative -space, one can consider its coinvariant subalgebras. If and then the coinvariant subalgebras represent (the formal duals of) quantum homogenous spaces of the (formal dual of) .
For example, a quotient Hopf algebra of , with quotient map , can be considered as representing a quantum subgroup. Then coacts on by map . The space of -coinvariants gives an example of a coinvariant subalgebra in .
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