Year: 2023
Type: preprint
Abstract: We introduce a natural generalization of the definition of a symmetric Hopf algebroid, internal to any symmetric monoidal category with coequalizers that commute with the monoidal product. Motivation for this is the study of Heisenberg doubles of countably dimensional Hopf algebras $A$ as internal Hopf algebroids over a (noncommutative) base $A$ in the category $\mathrm{indproVect}$ of filtered cofiltered vector spaces introduced by the author. One example of such Heisenberg double is internal Hopf algebroid $U(\mathfrak{g}) \sharp U(\mathfrak{g})^*$ over universal enveloping algebra $U(\mathfrak{g})$ of a finite-dimesional Lie algebra $\mathfrak{g}$ that is a properly internalized version of a completed Hopf algebroid previously studied as a Lie algebra type noncommutative phase space.
Source: arXiv (Cornell University)
Author: Stojić, Martina
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4386273113