# Codes, S-structures, and exceptional Lie algebras

## TL;DR

This paper explores the structure of exceptional Lie algebras E7 and E8, revealing their description via coordinate algebras that resemble code algebras, thus providing new insights into their algebraic properties.

## Contribution

It introduces optimal SL_2^n-structures for E7 and E8, connecting these Lie algebras to nonassociative code-like algebras for the first time.

## Key findings

- E7 and E8 have optimal SL_2^n-structures
- Their coordinate algebras resemble code algebras
- Provides a new algebraic framework for exceptional Lie algebras

## Abstract

The exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $SL_2^n$-structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so called code algebras.