Conformal Lie 2-algebras and conformal omni-Lie algebras

TL;DR

This paper introduces conformal Lie 2-algebras and conformal omni-Lie algebras, establishing their categorical equivalence and constructing examples from related algebraic structures.

Contribution

It defines new conformal algebraic structures and proves their categorical equivalence, expanding the theoretical framework of conformal algebra theory.

Findings

Category of conformal Lie 2-algebras is equivalent to 2-term conformal L-infinity algebras

Constructs conformal Lie 2-algebras from omni-Lie and Leibniz conformal algebras

Establishes foundational properties of conformal Lie 2-algebras

Abstract

The notions of conformal Lie 2-algebras and conformal omni-Lie algebras are introduced and studied. It is proved that the category of conformal Lie 2-algebras and the category of 2-term conformal $L_{\infty}$-algebras are equivalent. We construct conformal Lie 2-algebras from conformal omni-Lie algebras and Leibniz conformal algebras.