Non-standard matrix formats of Lie superalgebras

TL;DR

This paper explores alternative matrix formats for Lie superalgebras, focusing on the diagonal format, which appears in various advanced theoretical physics and algebraic applications.

Contribution

It introduces and analyzes the diagonal matrix format for Lie superalgebras, expanding beyond the traditional block partitioning approach.

Findings

Diagonal format naturally occurs in superconformal field theory

Applicable to super W-algebras and quantum supergroups

Provides new perspectives on matrix representations of Lie superalgebras

Abstract

The standard format of matrices belonging to Lie superalgebras consists of partitioning the matrices into even and odd blocks. In this paper, we study other possible matrix formats and in particular the so-called diagonal format which naturally occurs in various applications, e.g. in superconformal field theory, superintegrable models, for super W-algebras and quantum supergroups.