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Ω-Algebras with split products. / Pozhidaev, Aleksandr P.

In: Linear and Multilinear Algebra, Vol. 70, No. 16, 2022, p. 3054-3069.

Research output: Contribution to journal › Article › peer-review

Harvard

Pozhidaev, AP 2022, 'Ω-Algebras with split products', Linear and Multilinear Algebra, vol. 70, no. 16, pp. 3054-3069. https://doi.org/10.1080/03081087.2020.1822273

APA

Pozhidaev, A. P. (2022). Ω-Algebras with split products. Linear and Multilinear Algebra, 70(16), 3054-3069. https://doi.org/10.1080/03081087.2020.1822273

Vancouver

Pozhidaev AP. Ω-Algebras with split products. Linear and Multilinear Algebra. 2022;70(16):3054-3069. doi: 10.1080/03081087.2020.1822273

Author

Pozhidaev, Aleksandr P. / Ω-Algebras with split products. In: Linear and Multilinear Algebra. 2022 ; Vol. 70, No. 16. pp. 3054-3069.

BibTeX

@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.}",

note = "Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2022",

doi = "10.1080/03081087.2020.1822273",

language = "English",

volume = "70",

pages = "3054--3069",

journal = "Linear and Multilinear Algebra",

issn = "0308-1087",

publisher = "Taylor and Francis Ltd.",

number = "16",

}

RIS

TY - JOUR

T1 - Ω-Algebras with split products

AU - Pozhidaev, Aleksandr P.

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 -

ID: 25688357