A supergeometric approach to $L_{\infty}$-bialgebras

TL;DR

This paper introduces a supergeometric framework for defining and analyzing $L_{ olinebreak _{ olinebreak ext{infty}}}$-bialgebras and their Drinfeld doubles, extending previous algebraic structures with graded supergeometry techniques.

Contribution

It presents a novel supergeometric approach to $L_{ olinebreak _{ olinebreak ext{infty}}}$-bialgebras and constructs their Drinfeld doubles, advancing the theoretical understanding of these algebraic objects.

Findings

Defined $L_{ olinebreak _{ olinebreak ext{infty}}}$-bialgebras using graded supergeometry

Constructed Drinfeld doubles within this supergeometric framework

Extended algebraic structures with new geometric insights

Abstract

In this paper we use graded supergeometry to define and study $L_{\infty}$-bialgebras and their Drinfeld doubles a la Roytenberg & Voronov.