Lie-like Algebras (Superalgeras)

TL;DR

This paper introduces a new class of algebraic structures called Lie-like algebras and superalgebras, expanding the theoretical framework of algebraic systems.

Contribution

It defines Lie-like algebras and superalgebras for various types, providing a foundational extension to existing algebraic theories.

Findings

Defined Lie-like algebras for different types

Extended algebraic theory to superalgebras

Laid groundwork for future algebraic research

Abstract

We introduce the notion of a Lie-like algebra$^{\diamond}$ (superalgebra$^{\diamond}$) for $\diamond\in\{^{1-st}, ^{2-nd}, ^{3-rd} \}$.