Symmetries of Algebras Captured by Actions of Weak Hopf Algebras: Symmetries of Algebras Captured by Actions: F. Calderón et al.

In this paper, we present a generalization of well-established results regarding symmetries of k -algebras, where k is a field. Traditionally, for a k -algebra A, the group of k -algebra automorphisms of A captures the symmetries of A via group actions. Similarly, the Lie algebra of derivations of A captures the symmetries of A via Lie algebra actions. In this paper, given a category C whose objects possess k -linear monoidal categories of modules, we introduce an objec Sym C (A) that captures the symmetries of A via actions of objects in C . Our study encompasses various categories whose objects include groupoids, Lie algebroids, and more generally, cocommutative weak Hopf algebras. Notably, we demonstrate that for a positively graded non-connected k -algebra A, some of its symmetries are naturally captured within the weak Hopf framework. [ABSTRACT FROM AUTHOR]