Splints of root systems of Lie superalgebras

TL;DR

This paper extends the concept of splints from root systems of simple Lie algebras to classical Lie superalgebras, facilitating the study of embeddings and branching rules relevant in physics.

Contribution

It introduces the notion of splints for classical Lie superalgebras, broadening the applicability of root system analysis in mathematical physics.

Findings

Extended splint concept to classical Lie superalgebras

Simplified calculation of branching coefficients

Enhanced understanding of algebra embeddings

Abstract

Splints of root system of simple lie algebras appears naturally on studies of embedding of reductive subalgebras. A splint can be used to construct a branching rules as implementation of this idea simplifies calculation of branching coefficient. We extend the concept of splints to classical lie superalgebras cases as these algebras have wide application in physics.