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This paper demonstrates the absence of non-trivial ultra derivations and structures in ultra algebras.
In this paper, we introduce transposed Poisson structures on the Heisenberg-Virasoro ultra algebra. We obtain a result that tells us that there are no non-trivial 1/2-ultra derivations on the Heisenberg-Virasoro ultra algebra and, as a consequence, we show that there are no non-trivial transposed Poisson ultra algebra structures defined on the Heisenberg-Virasoroultra algebra.
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Andrade et al. (2025) studied this question.
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