This article is cited in 2 papers

Mathematical logic, algebra and number theory

Gelfand–Dorfman–Novikov–Poisson superalgebras and their envelopes

A. S. Zakharov<sup>ab

a</sup> Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
^b Novosibirsk State Technical University, 20, K. Marksa ave., Novosibirsk, 630073, Russia

Abstract: We prove some result of $\mathcal{GDNP}$–algebras for $\mathcal{GDNP}$–superalgebras and embeding some $\mathcal{GDNP}$–superalgebras into $\mathcal{GDNP}$–superalgebras of vector type. Also we prove that not every $\mathcal{GDNP}$–superalgebra can be embeded into associative supercommutative superalgebra with even derivation $D$ and product given by $a\circ b=a D(b)$.

Keywords: Gelfand-Dorfman-Novikov-Poisson superalgebras, derivations of algebras, Jordan superalgebras.

UDC: 512.554

MSC: 17A70

Received September 24, 2019, published December 5, 2019

DOI: 10.33048/semi.2019.16.131

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