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V-universal Hopf algebras (co)acting on Ω-algebrasстатья Исследовательская статья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Agore Ana, Gordienko A.S., Vercruysse J.
- Журнал: Communications in Contemporary Mathematics
- Том: 25
- Номер: 01
- Год издания: 2023
- Издательство: World Scientific Publishing Co
- Местоположение издательства: Singapore
- Первая страница: 2150095-1
- Последняя страница: 2150095-40
- Номер статьи: 2150095
- DOI: 10.1142/s0219199721500954
- Аннотация: We develop a theory which unifies the universal (co)acting bi/Hopf algebras as studied by Sweedler, Manin and Tambara with the recently introduced [A. L. Agore, A. S. Gordienko and J. Vercruysse, On equivalences of (co)module algebra structures over Hopf algebras, J. Noncommut. Geom., doi: 10.4171/JNCG/428.] bi/Hopf-algebras that are universal among all support equivalent (co)acting bi/Hopf algebras. Our approach uses vector spaces endowed with a family of linear maps between tensor powers of A, called Ω-algebras. This allows us to treat algebras, coalgebras, braided vector spaces and many other structures in a unified way. We study V-universal measuring coalgebras and V-universal comeasuring algebras between Ω-algebras A and B, relative to a fixed subspace V of Vect(A,B). By considering the case A = B, we derive the notion of a V-universal (co)acting bialgebra (and Hopf algebra) for a given algebra A. In particular, this leads to a refinement of the existence conditions for the Manin–Tambara universal coacting bi/Hopf algebras. We establish an isomorphism between the V-universal acting bi/Hopf algebra and the finite dual of the V-universal coacting bi/Hopf algebra under certain conditions on V in terms of the finite topology on EndF(A).
- Добавил в систему: Гордиенко Алексей Сергеевич