Work

Semi-abelian condition for color Hopf algebras

Year: 2024

Type: article

Abstract: Recently, in [22], it was shown that the category of cocommutative Hopf algebras over an arbitrary field k is semi-abelian. We extend this result to the category of cocommutative color Hopf algebras, i.e. of cocommutative Hopf monoids in the symmetric monoidal category of G-graded vector spaces with G an abelian group, given an arbitrary skew-symmetric bicharacter on G, when G is finitely generated and the characteristic of k is different from 2 (not needed if G is finite of odd cardinality). We also prove that this category is action representable and locally algebraically cartesian closed, then algebraically coherent. In particular, these results hold for the category of cocommutative super Hopf algebras by taking G=Z2. Furthermore, we prove that, under the same assumptions on G and k, the abelian category of abelian objects in the category of cocommutative color Hopf algebras is given by those cocommutative color Hopf algebras which are also commutative.

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2024.107677

Author: Andrea Sciandra

Institution: University of Turin

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,330

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni