TY - JOUR

T1 - A Class of Generalized Derivations

AU - Zakharov, A. S.

N1 - Supported by Russian Science Foundation, project No. 21-11-00286. Публикация для корректировки.

PY - 2023/1

Y1 - 2023/1

N2 - We consider a class of generalized derivations that arise in connection with the problem of adjoining unity to an algebra with generalized derivation, and of searching envelopes for Novikov–Poisson algebras. Conditions for the existence of the localization of an algebra with ternary derivation are specified, as well as conditions under which given an algebra with ternary derivation, we can construct a Novikov–Poisson algebra and a Jordan superalgebra. Finally, we show how the simplicity of an algebra with Brešar generalized derivation is connected with simplicity of the appropriate Novikov algebra.

AB - We consider a class of generalized derivations that arise in connection with the problem of adjoining unity to an algebra with generalized derivation, and of searching envelopes for Novikov–Poisson algebras. Conditions for the existence of the localization of an algebra with ternary derivation are specified, as well as conditions under which given an algebra with ternary derivation, we can construct a Novikov–Poisson algebra and a Jordan superalgebra. Finally, we show how the simplicity of an algebra with Brešar generalized derivation is connected with simplicity of the appropriate Novikov algebra.

KW - Jordan superalgebra

KW - Novikov–Poisson algebra

KW - differential algebra

KW - generalized derivation

KW - ternary derivation

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85175657204&origin=inward&txGid=eb55bc17592a604ebac541de6b56c9c9

UR - https://www.mendeley.com/catalogue/170c8413-6705-38f1-8d1b-7cac4bef5b44/

U2 - 10.1007/s10469-023-09713-2

DO - 10.1007/s10469-023-09713-2

M3 - Article

VL - 61

SP - 466

EP - 480

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -