U. of Haifa Algebra seminar, December 3, 2020
Speaker: Alexey Gordienko (Moscow State University)
Topic: Equivalences of (co)module structures and V-universal
(co)acting bi/Hopf algebras
Place: This is an online seminar. Please email Yuval Ginosar “ginosar at math dot haifa dot ac dot il” for the Zoom ID and password.
Date: Thursday, December 3, 2020
It turns out that for many applications (say, if we study
H-sub(co)modules, H-invariant ideals, polynomial H-identities…) it
is not really important, which particular Hopf algebra is (co)acting
on a given H-(co)module algebra. Here we come naturally to the notion
of (support) equivalence of Hopf (co)module structures on algebras which is the direct generalization of the notion of (weak) equivalence of group gradings.
In addition, among all Hopf algebras that realize a given Hopf
(co)module structure there are distinguished ones which we call
universal Hopf algebras. One can develop a unified theory of so called
V-universal bi/Hopf algebras that embraces the universal bi/Hopf
algebras of given (co)module structures and the universal bi/Hopf
algebras introduced by Sweedler, Manin and Tambara.
On one hand, this enables to refine the existence conditions for the
Manin-Tambara universal Hopf algebras. On the other hand, this
approach makes it possible to establish a certain duality between the
V-universal acting and coacting bi/Hopf algebras. In the talk we will
discuss this theory as well as its possible applications.
(Joint project with Ana Agore and Joost Vercruysse.)