engleski

Scalar extension Hopf algebroids

Given a Hopf algebra H, Brzezinski and Militaru have shown that each braided commutative Yetter-Drinfeld H-module algebra A gives rise to an associative A-bialgebroid structure on the smash product algebra A#H. They also exhibited an antipode map making A#H the total algebra of a Lu’s Hopf algebroid over A. 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 A and A^op of braided commutative Yetter-Drinfeld H-module algebras, and output is a symmetric Hopf algebroid A#H = H#A^op over A. This construction does not require that the antipode of H is invertible.

Hopf algebroid ; antipode ; Brzezinski-Militaru theorem ; scalar extension ; bialgebroid

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