# Metric derived from Lie Groups

## TL;DR

This paper derives a metric from Lie groups and conjectures that classical Lie groups' metrics become Einstein metrics, providing insights into geometric structures associated with these groups.

## Contribution

It presents explicit expressions for metrics derived from Lie groups and conjectures their Einstein property for classical groups.

## Key findings

- Derived explicit metrics from Lie groups.
- Conjectured Einstein property for classical Lie group metrics.
- Provides a foundation for further geometric analysis of Lie groups.

## Abstract

We give the expression of the metric derived from Lie groups. For the metric derived from classical Lie groups such as the unitary group, the orthogonal group and the symplectic group, we conjecture that the metric becomes the Einstein metric.