# Generalized symmetry in noncommutative (complex) geometry

## TL;DR

This paper develops a broad framework for noncommutative complex geometry using Hopf algebroid covariance, extending previous models and including examples like transverse complex and Kähler structures.

## Contribution

It introduces Hopf algebroid covariance into noncommutative differential calculus, creating a more general geometric framework that encompasses prior approaches.

## Key findings

- Developed a general framework for noncommutative complex geometry.
- Presented examples including transverse complex and Kähler structures.
- Connected the new framework with existing literature.

## Abstract

We introduce Hopf algebroid covariance on Woronowicz's differential calculus. Using it, we develop quite a general framework of noncommutative complex geometry that subsumes the one in [2]. We present transverse complex and K\"ahler structures as examples and discuss several other examples. Relation with past literature is described.