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Hopf Pairings and (Co)induction Functors over Commutative Rings

Summary: Hopf Pairings and (Co)induction Functors over
Commutative Rings
Jawad Y. Abuhlail
Mathematics Department
Birzeit University
P.O.Box 14, Birzeit - Palestine
(Co)induction functors appear in several areas of Algebra in different forms. In-
teresting examples are the so called induction functors in the Theory of Affine Al-
gebraic Groups. In this paper we investigate Hopf pairings (bialgebra pairings) and
use them to study (co)induction functors for affine group schemes over arbitrary
commutative ground rings. We present also a special type of Hopf pairings (bialge-
bra pairings) satisfying the so called -condition. For those pairings the coinduction
functor is studied and nice descriptions of it are obtained. Along the paper several
interesting results are generalized from the case of base fields to the case of arbitrary
commutative (Noetherian) ground rings.
Hopf pairings (respectively bialgebra pairings) were presented by M. Takeuchi [35, Page
15] (respectively S. Majid [26, 1.4]). With the help of these, several authors studied affine
group schemes and quantum groups over arbitrary commutative ground rings (e.g. [16],


Source: Abuhlail, Jawad Younes - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals


Collections: Mathematics