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$δ$-Poisson and transposed $δ$-Poisson algebras
[Submitted on 8 Nov 2024 (v1), last revised 2 Jun 2026 (this ver · 2026-06-03 · via math updates on arXiv.org

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Abstract:We present a comprehensive study of two new Poisson-type algebras. Namely, we are working with $\delta$-Poisson and transposed $\delta$-Poisson algebras. Our research shows that these algebras are related to many interesting identities. In particular, they are related to shift associative algebras, $F$-manifold algebras, algebras of Jordan brackets, etc. We classify simple $\delta$-Poisson and transposed $\delta$-Poisson algebras and found their depolarizations. We study $\delta$-Poisson and mixed-Poisson algebras to be Koszul and self-dual. Bases of the free $\delta$-Poisson and mixed-Poisson algebras generated by a countable set $X$ are constructed.

Submission history

From: Ivan Kaygorodov [view email]
[v1] Fri, 8 Nov 2024 11:43:30 UTC (26 KB)
[v2] Tue, 2 Jun 2026 13:48:24 UTC (26 KB)