Given a field , a -vector space pairing between -bialgebras and is a -linear map such that
(where on the left hand side denotes the map given by ), is called the bialgebra pairing.
The bialgebra pairing which is perfect as -vector space pairing (i. e. if implies that either or is ) is called the bialgebra duality.
If and are Hopf algebras then the compatibility with antipodes is .
Revised on February 9, 2016 07:25:06
by Tim Porter