Ω-Algebras with split products

Aleksandr P. Pozhidaev

doi:10.1080/03081087.2020.1822273

Ω-Algebras with split products

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

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

Доступ к документу

10.1080/03081087.2020.1822273

Link to publication in Scopus

Цитировать

@article{35bf39a67a584024b748fb9357535d3b,

title = "Ω-Algebras with split products",

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.",

keywords = "17D15, associative pair, Bol algebra, Dialgebra, Eilenberg bimodule, Filippov algebra, Primary 17A42, right-alternative algebra, Secondary 17A30, simple dialgebra, Ω-sp-algebra, DIALGEBRAS, Omega-sp-algebra",

author = "Pozhidaev, {Aleksandr P.}",

year = "2020",

month = sep,

day = "20",

doi = "10.1080/03081087.2020.1822273",

language = "English",

journal = "Linear and Multilinear Algebra",

issn = "0308-1087",

publisher = "Taylor and Francis Ltd.",

}

TY - JOUR

T1 - Ω-Algebras with split products

AU - Pozhidaev, Aleksandr P.

PY - 2020/9/20

Y1 - 2020/9/20

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

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

ER -

Ω-Algebras with split products

Аннотация

Доступ к документу

Fingerprint

Цитировать