Defining relations and flip Dynkin superdiagrams

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 \inδsequences. We have got the defining relations for the both the Dynkin diagrams and flip Dynkin diagrams.

arXiv commentpreliminary version