Principal SUSY and nonSUSY W-algebras and their Zhu algebras
Naoki Genra, Arim Song, Uhi Rinn Suh

TL;DR
This paper proves the supersymmetry of certain W-algebras associated with Lie superalgebras and establishes their isomorphism with Zhu algebras, advancing understanding of their algebraic structures and symmetries.
Contribution
It demonstrates the isomorphism between principal SUSY and nonSUSY W-algebras and their Zhu algebras, revealing new structural insights.
Findings
W-algebra $W^k(rak{g},F)$ is isomorphic to SUSY W-algebra via screening operators
Finite SUSY W-algebras are isomorphic to Zhu algebras of SUSY W-algebras
Finite SUSY principal W-algebra is isomorphic to finite principal W-algebra
Abstract
This paper consists of two parts. In the first part, we prove that when is a simple basic Lie superalgebra with a principal odd nilpotent element , the W-algebra for is isomorphic to the SUSY W-algebra via screening operators, which implies the supersymmetry of . In the second part, we show that a finite SUSY W-algebra, which is a Hamiltonian reduction of for the SUSY Takiff algebra is isomorphic to the Zhu algebra of a SUSY W-algebra. As a corollary, we show that a finite SUSY principal W-algebra is isomorphic to a finite principal W-algebra.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topics in Algebra · Fuzzy and Soft Set Theory
