Invariant Algebras

TL;DR

This paper introduces the concept of invariant algebras and their representations, providing methods to construct various algebraic structures such as Lie, Jordan, Leibniz, pre-Lie, and left-symmetric algebras within this framework.

Contribution

It presents the novel concept of invariant algebras and offers multiple construction techniques for diverse algebraic systems using these invariants.

Findings

Defined invariant algebras and their representations.

Provided methods to construct Lie, Jordan, Leibniz, pre-Lie, and left-symmetric algebras.

Established new links between invariant algebras and classical algebraic structures.

Abstract

We introduce invariant algebras and representation$^{(c_1,..., c_8)}$ of algebras, and give many ways of constructing Lie algebras, Jordan algebras, Leibniz algebras, pre-Lie algebras and left-symmetric algebras in an invariant algebras.