TY - JOUR

T1 - Ω-Algebras with split products

AU - Pozhidaev, Aleksandr P.

N1 - Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2022

Y1 - 2022

N2 - We introduce Ω-sp-algebras as a generalization of dialgebras to the case of Ω-algebras. Given a variety of algebras (Formula presented.), we provide a criterion for an Ω-sp-algebra to be a (Formula presented.) -sp-algebra. We give examples of Ω-sp-algebras such as associative sp-systems, ternary Filippov sp-algebras, Lie triple sp-systems, and Bol sp-algebras. We prove a lifting theorem for the term functor and the triviality of every simple Ω-sp-algebra.

AB - We introduce Ω-sp-algebras as a generalization of dialgebras to the case of Ω-algebras. Given a variety of algebras (Formula presented.), we provide a criterion for an Ω-sp-algebra to be a (Formula presented.) -sp-algebra. We give examples of Ω-sp-algebras such as associative sp-systems, ternary Filippov sp-algebras, Lie triple sp-systems, and Bol sp-algebras. We prove a lifting theorem for the term functor and the triviality of every simple Ω-sp-algebra.

KW - 17D15

KW - associative pair

KW - Bol algebra

KW - Dialgebra

KW - Eilenberg bimodule

KW - Filippov algebra

KW - Primary 17A42

KW - right-alternative algebra

KW - Secondary 17A30

KW - simple dialgebra

KW - Ω-sp-algebra

KW - DIALGEBRAS

KW - Omega-sp-algebra

UR - http://www.scopus.com/inward/record.url?scp=85091144667&partnerID=8YFLogxK

U2 - 10.1080/03081087.2020.1822273

DO - 10.1080/03081087.2020.1822273

M3 - Article

AN - SCOPUS:85091144667

VL - 70

SP - 3054

EP - 3069

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 16

ER -