# Classification of bases of twisted affine root supersystems

@article{Yousofzadeh2019ClassificationOB,
title={Classification of bases of twisted affine root supersystems},
journal={Journal of Algebraic Combinatorics},
year={2019},
volume={55},
pages={919 - 978}
}
• 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

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
• Mathematics
• 2011
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
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.
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
• Mathematics, Art
Journal of Algebra and Its Applications
• 2018
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
• Mathematics
Revista Matemática Iberoamericana
• 2020
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
• Mathematics
• 2007
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)