6533b871fe1ef96bd12d1a15

RESEARCH PRODUCT

The dual and the double of a Hopf algebroid are Hopf algebroids

Peter Schauenburg

subject

[ MATH ] Mathematics [math]Pure mathematicsGeneral Computer ScienceDuality (optimization)01 natural sciencesTheoretical Computer ScienceMathematics::Category TheoryMathematics::Quantum AlgebraMathematics - Quantum Algebra0103 physical sciencesFOS: Mathematics[MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA]Quantum Algebra (math.QA)[ MATH.MATH-CT ] Mathematics [math]/Category Theory [math.CT]0101 mathematics[MATH]Mathematics [math]Hopf algebroid[MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT]Mathematics[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA]Algebra and Number TheoryMSC: 16T99 18D10[ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA]010308 nuclear & particles physicsbialgebroid[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]010102 general mathematicsMathematics::Rings and AlgebrasSkewMathematics - Rings and Algebras[MATH.MATH-CT] Mathematics [math]/Category Theory [math.CT][ MATH.MATH-RA ] Mathematics [math]/Rings and Algebras [math.RA]Dual (category theory)Rings and Algebras (math.RA)Theory of computation[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]duality

description

Let $H$ be a $\times$-bialgebra in the sense of Takeuchi. We show that if $H$ is $\times$-Hopf, and if $H$ fulfills the finiteness condition necessary to define its skew dual $H^\vee$, then the coopposite of the latter is $\times$-Hopf as well. If in addition the coopposite $\times$-bialgebra of $H$ is $\times$-Hopf, then the coopposite of the Drinfeld double of $H$ is $\times$-Hopf, as is the Drinfeld double itself, under an additional finiteness condition.

yearjournalcountryeditionlanguage
2017-02-01
https://hal.science/hal-01144711