Classification of bases of twisted affine root supersystems

@article{Yousofzadeh2019ClassificationOB,
  title={Classification of bases of twisted affine root supersystems},
  author={Malihe Yousofzadeh},
  journal={Journal of Algebraic Combinatorics},
  year={2019},
  volume={55},
  pages={919 - 978}
}
  • M. Yousofzadeh
  • Published 6 October 2019
  • Mathematics
  • Journal of Algebraic Combinatorics
Following the definition of a root basis of an affine root system, we define a base of the root system R of an affine Lie superalgebra to be a linearly independent subset B of the linear span of R such that B⊆R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B\subseteq R$$\end{document} and each root can be written… 

References

SHOWING 1-10 OF 21 REFERENCES

Extended Affine Root Supersystems

Generalized reflection root systems

On generalizations of root systems

We define a generalization of a root system as a set of vectors in a vector space with some symmetry property. The main difference with the usual root systems is the existence of isotropic roots. We

Developments and trends in infinite-dimensional Lie theory

Preface.- Part A: Infinite-Dimensional Lie (Super-)Algebras.- Isotopy for Extended Affine Lie Algebras and Lie Tori.- Remarks on the Isotriviality of Multiloop Algebras.- Extended Affine Lie Algebras

Infinite Dimensional Lie Algebras

Introduction Notational conventions 1. Basic definitions 2. The invariant bilinear form and the generalized casimir operator 3. Integrable representations of Kac-Moody algebras and the weyl group 4.

SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH

We classify the simple graded Lie algebras , for which the dimension of the space grows as some power of , under the additional assumption that the adjoint representation of on is irreducible. From

On ω-Lie superalgebras

Let [Formula: see text] be a finite-dimensional vector space over a field [Formula: see text] of characteristic zero, [Formula: see text] an anti-commutative product on [Formula: see text] and

Highest weight modules for affine Lie superalgebras

We describe Borel and parabolic subalgebras of affine Lie superalgebras and study the Verma type modules associated to such subalgebras. We give necessary and sufficient conditions under which these

Classification of Finite-Growth General Kac–Moody Superalgebras

A contragredient Lie superalgebra is a superalgebra defined by a Cartan matrix. A contragredient Lie superalgebra has finite-growth if the dimensions of the graded components (in the natural grading)