Defining relations and flip Dynkin superdiagrams

TL;DR

This paper introduces flip Dynkin superdiagrams for Lie superalgebras, establishing a correspondence between fermionic and bosonic roots, and constructs all such diagrams to explore their algebraic structures.

Contribution

It constructs all flip Dynkin superdiagrams for Lie superalgebras, revealing new classes of Borel subalgebras and non-isomorphic diagrams via  sequences.

Findings

Established correspondence between fermionic and bosonic roots.

Constructed all flip Dynkin superdiagrams for Lie superalgebras.

Derived defining relations for both standard and flip diagrams.

Abstract

The motivation comes from boson fermion correspondence. This article shows for each fermionic root there is correspondence a bosonic root, as a result we get for each Dynkin diagram of Lie Superalgebra a corresponding flip Dynkin Superdiagram. This article construct all the filp Dynkin Superdiagrams of Lie superalgebras(LS). This can create non conjugate classes Borel subalgebra (subsuperalgebras) or non isomorphic Dynkin diagrams of LS using \in\delta sequences. We have got the defining relations for the both the Dynkin diagrams and flip Dynkin diagrams.