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On the root system of a Kac-Moody superalgebra

Maria Gorelik, Shay Kinamon Kerbis

Abstract

In this paper we extend several results about root systems of Kac-Moody algebras to superalgebra context. In particular, we describe the root bases and the sets of imaginary roots.

On the root system of a Kac-Moody superalgebra

Abstract

In this paper we extend several results about root systems of Kac-Moody algebras to superalgebra context. In particular, we describe the root bases and the sets of imaginary roots.
Paper Structure (93 sections, 159 equations)

This paper contains 93 sections, 159 equations.

Table of Contents

  1. Introduction
  2. Skeleton
  3. Root systems
  4. Classification
  5. Root systems of Kac-Moody superalgebras
  6. Root bases
  7. Imaginary roots
  8. Algebra $\mathfrak g(B_{\pi})$
  9. Group $\operatorname{Sk}^D(v)$
  10. The group $\operatorname{Sp}^D(v)$ for the Kac-Moody superalgebras
  11. The group $\operatorname{Sk}^D(v)$ for type (Aff)
  12. Content of the paper
  13. Acknowledgement
  14. Index of definitions and notation
  15. Preliminaries
  16. ...and 78 more sections

Theorems & Definitions (29)

  • proof
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  • ...and 19 more