Good gradings of basic Lie superalgebras
Crystal Hoyt
TL;DR
This paper classifies good Z-gradings of basic Lie superalgebras over algebraically closed fields of characteristic zero, which are crucial in quantum Hamiltonian reduction and the construction of super W-algebras.
Contribution
It provides a comprehensive classification of good Z-gradings for basic Lie superalgebras and describes centralizers of nilpotent elements and sl(2)-triples.
Findings
Classification of good Z-gradings for basic Lie superalgebras.
Description of centralizers of nilpotent even elements.
Analysis of centralizers of sl(2)-triples in gl(m|n) and osp(m|2n).
Abstract
We classify good Z-gradings of basic Lie superalgebras over an algebraically closed field of characteristic zero. Good Z-gradings are used in quantum Hamiltonian reduction for affine Lie superalgebras, where they play a role in the construction of super W-algebras. We also describe the centralizer of a nilpotent even element and of an sl(2)-triple in gl(m|n) and osp(m|2n).
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons