We introduce the notion of quantum-symmetric equivalence of two connected graded
algebras, based on Morita–Takeuchi equivalences of their universal quantum groups, in the …

The universal (co) acting bi/Hopf algebras introduced by Yu.\, I.~ Manin, M.~ Sweedler and
D.~ Tambara, the universal Hopf algebra of a given (co) module structure, as well as the …

For a bialgebra L coacting on ak-algebra A, a classical result states A is a right L-comodule
algebra if and only if A is an algebra in the category ML of right L-comodules. We generalize …

Prompted by an inquiry of Manin on whether a coacting Hopf-type structure H and an
algebra A that is coacted upon share algebraic properties, we study the particular case of A …

We show that if two $ m $-homogeneous algebras have Morita equivalent graded module
categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal …

We introduce the universal algebra of two Poisson algebras P and Q as a commutative
algebra A:= P (P, Q) satisfying a certain universal property. The universal algebra is shown …

In this paper, we present a generalization of well-established results regarding symmetries
of k-algebras, where k is a field. Traditionally, for ak-algebra A, the group of k-algebra …

This thesis investigates the properties of weak bialgebras and weak Hopf algebras, their (co)
representations, and applications in groupoids, path algebras, and Lie algebroids. The …

Uma extensão de Ore é, essencialmente, uma estrutura de anel no módulo livre A [X], onde
os elementos de A não necessariamente comutam com a indeterminada X e para a qual …

This thesis investigates the properties of weak bialgebras and weak Hopf algebras, their (co)
representations, and applications in groupoids, path algebras, and Lie algebroids. The …