Invariant and non-invariant almost complex structures on compact quotients of Lie groups

TL;DR

This paper surveys the existence of invariant and non-invariant almost complex structures on compact Lie group quotients, highlighting differences in their properties and providing new examples of Kodaira dimension calculations.

Contribution

It offers a comparative analysis of invariant and non-invariant structures and introduces new computations of Kodaira dimensions for these structures.

Findings

Invariant and non-invariant structures exhibit different behaviors.

New examples of Kodaira dimension computations are provided.

The study enhances understanding of complex structures on Lie group quotients.

Abstract

In this paper we briefly survey the classical problem of understanding which Lie algebras admit a complex structure, put in the broader perspective of almost complex structures with special properties. We focus on the different behavior of invariant and non-invariant structures, with a special attention to their canonical bundle and Kodaira dimension. We provide new examples of computations of Kodaira dimension of invariant and non-invariant structures.