Ω-Algebras with split products

Aleksandr P. Pozhidaev

doi:10.1080/03081087.2020.1822273

Ω-Algebras with split products

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Аннотация

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.

Язык оригинала	английский
Число страниц	16
Журнал	Linear and Multilinear Algebra
Ранняя дата в режиме онлайн	20 сен 2020
DOI	https://doi.org/10.1080/03081087.2020.1822273
Состояние	Электронная публикация перед печатью - 20 сен 2020

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10.1080/03081087.2020.1822273

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abstract = "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.",

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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.

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KW - associative pair

KW - Bol algebra

KW - Dialgebra

KW - Eilenberg bimodule

KW - Filippov algebra

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KW - right-alternative algebra

KW - Secondary 17A30

KW - simple dialgebra

KW - Ω-sp-algebra

KW - DIALGEBRAS

KW - Omega-sp-algebra

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JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

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Ω-Algebras with split products

Аннотация

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