Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structures via the representation theory of families of algebras. This paper examines a fundamental construction in group theory, the direct product, and how it can be used to build representation theoretic Hopf algebras out of towers of groups. A key special case gives us the noncommutative symmetric functions NSym, but there are many things that we can say for the general Hopf algebras, including the structure of their character groups and a formula for the antipode.
@article{10_37236_11259,
author = {Farid Aliniaeifard and Nathaniel Thiem},
title = {Hopf structures in the representation theory of direct products},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {4},
doi = {10.37236/11259},
zbl = {1509.05180},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11259/}
}
TY - JOUR
AU - Farid Aliniaeifard
AU - Nathaniel Thiem
TI - Hopf structures in the representation theory of direct products
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/11259/
DO - 10.37236/11259
ID - 10_37236_11259
ER -
%0 Journal Article
%A Farid Aliniaeifard
%A Nathaniel Thiem
%T Hopf structures in the representation theory of direct products
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/11259/
%R 10.37236/11259
%F 10_37236_11259
Farid Aliniaeifard; Nathaniel Thiem. Hopf structures in the representation theory of direct products. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/11259
