Scalar extension Hopf algebroids
Martina Stoji\'c

TL;DR
This paper completes the proof that the antipode in certain Hopf algebroids is an antihomomorphism and introduces a generalized construction for symmetric Hopf algebroids that does not require the antipode to be invertible.
Contribution
It provides a complete proof of the antipode's antihomomorphism property and introduces a new generalized construction of symmetric Hopf algebroids without assuming invertibility of the antipode.
Findings
Complete proof of the antipode antihomomorphism property.
A new generalized construction of symmetric Hopf algebroids.
Construction does not require invertibility of the antipode.
Abstract
Given a Hopf algebra , Brzezi\'nski and Militaru have shown that each braided commutative Yetter-Drinfeld -module algebra gives rise to an associative -bialgebroid structure on the smash product algebra . They also exhibited an antipode map making the total algebra of a Lu's Hopf algebroid over . However, the published proof that the antipode is an antihomomorphism covers only a special case. In this paper, a complete proof of the antihomomorphism property is exhibited. Moreover, a new generalized version of the construction is provided. Its input is a compatible pair and of braided commutative Yetter-Drinfeld -module algebras, and output is a symmetric Hopf algebroid over . This construction does not require that the antipode of is invertible.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
