Research output: Contribution to journal › Article › peer-review
A Class of Generalized Derivations. / Zakharov, A. S.
In: Algebra and Logic, Vol. 61, No. 6, 01.2023, p. 466-480.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 59192763