What question did this study set out to answer?

This research aims to analyze the existence of transposed Poisson structures and derivations in q-analog algebras under specific conditions.

June 20, 2026

Transposed Poisson Structures on the q -Analog Virasoro-like Algebras and q -Quantum Torus Lie Algebras

Key Points

This research aims to analyze the existence of transposed Poisson structures and derivations in q-analog algebras under specific conditions.
Investigated transposed Poisson structures on q-analog Virasoro-like and quantum torus Lie algebras.
Classified cases based on the generic nature of q and its properties as a primitive root of unity.
Deduced the existence of non-trivial structures and derivations for both algebra types.
For generic q, no non-trivial transposed Poisson structures exist on the Virasoro-like algebra.
The quantum torus Lie algebra has non-trivial q-derivations but no transposed Poisson structure when q is generic.
When q is a primitive root of unity, both algebras have non-trivial q-derivations, with a specific non-trivial transposed Poisson structure for the Virasoro-like algebra.

Abstract

We investigate the transposed Poisson structures on both the Formula: see text-analog Virasoro-like algebra and Formula: see text-quantum torus Lie algebra considering the cases where Formula: see text is generic and where Formula: see text is a primitive root of unity, respectively. We establish the following results: When Formula: see text is generic, there are no non-trivial Formula: see text-derivations and consequently, no non-trivial transposed Poisson algebra structures exist on the Formula: see text-analog Virasoro-like algebra. Meanwhile, the Formula: see text-quantum torus Lie algebra does possess non-trivial Formula: see text-derivations but lacks of a non-trivial transposed Poisson structure. When Formula: see text is a primitive root of unity, both the Formula: see text-analog Virasoro-like algebra and the Formula: see text-quantum torus Lie algebra possess non-trivial Formula: see text-derivations. We present the non-trivial transposed Poisson algebra structure for the Formula: see text-analog Virasoro-like algebra. However, the Formula: see text-quantum torus Lie algebra lacks of a non-trivial transposed Poisson structure.

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Cite This Study

Lin et al. (Fri,) studied this question.

synapsesocial.com/papers/6a362f63db0793dc1a536db1 https://doi.org/https://doi.org/10.1142/s0219498827502744

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