November 30, 2025

Partial Hopf actions on generalized matrix algebras

Puntos clave

The existence of necessary and sufficient conditions for the action of a Hopf algebra on a matrix algebra was established.
Specific cases were explored where the Hopf algebra is a group algebra, recovering previous conditions for unital actions.
The analysis introduced the concept of opposite covariant pairs, showcasing a universal property related to partial actions.
Findings may aid in understanding the structure of matrix algebras under algebraic actions, emphasizing their mathematical significance.

Resumen

Abstract Let be a field, H a Hopf algebra over, and R = (ᵢMⱼ) ₁ ₈, ₉ ₍ a generalized matrix algebra. In this work, we establish necessary and sufficient conditions for H to act partially on R. To achieve this, we introduce the concept of an opposite covariant pair and demonstrate that it satisfies a universal property. In the special case where H = G is the group algebra of a group G, we recover the conditions given in 7 for the existence of a unital partial action of G on R.

Me gusta

Guardar

Cite This Study

Bagio et al. (Wed,) studied this question.

synapsesocial.com/papers/692b9d7b1d383f2b2a379479 https://doi.org/https://doi.org/10.1017/s0017089525100852

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Me gusta

Guardar