(Transposed) Poisson algebra structures on null-filiform associative algebras

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arxiv 2503.06295 v1 pith:X44JGARL submitted 2025-03-08 math.RA

Jobir Adashev , Xursanoy Berdalova , Feruza Toshtemirova This is my paper

classification math.RA

keywords algebraalgebrasassociativenull-filiformpoissontransposedassociatedclassifications

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In this paper we investigate classifications of all (transposed) Poisson algebras of the associated associative null-filiform algebra

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$\sigma$-matching and interchangeable structures on truncated polynomial algebras
math.RA 2026-03 accept novelty 5.5 of 10

On null-filiform associative algebras, id-matching, interchangeable and totally compatible products coincide and are classified into the families B1 and Bs(α); (12)-matching products form several further families Ai.
Transposed $\delta$-Poisson algebra structures on null-filiform associative algebras
math.RA 2025-06 conditional novelty 5.0 of 10

All transposed δ-Poisson structures on null-filiform associative algebras are classified, with special behavior exactly at δ=0,1,2.