Transposed \delta-Poisson (super)algebra Structures on the Virasoro-like algebra and its Kantor Lie-double
Jie Lin, Chengyu Liu, Jingjing Jiang
TL;DR
This paper investigates transposed ta-Poisson (super)algebra structures on the Virasoro-like algebra and its Kantor Lie-double, concluding that such structures are absent despite the existence of non-trivial ta-derivations only at ta=1.
Contribution
It provides a detailed analysis of transposed ta-Poisson (super)algebra structures on these algebras and establishes their non-existence, clarifying the algebraic landscape.
Findings
Non-trivial ta-derivations exist only at ta=1.
No non-trivial transposed ta-Poisson (super)algebra structures are found.
The study enhances understanding of algebraic structures related to the Virasoro-like algebra.
Abstract
We undertake a study of transposed \delta-Poisson (super)algebra structures on the Virasoro-like algebra and its Kantor Lie-double -- the latter being constructed via Kantor's procedure. This work leads to the finding that, whereas non-trivial \delta-derivations exist solely at \delta=1, non-trivial transposed \delta-Poisson (super)algebra structures are entirely absent.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models