On a ternary generalization of Jordan algebras

Standard

On a ternary generalization of Jordan algebras. / Kaygorodov, Ivan; Pozhidaev, Alexander; Saraiva, Paulo.

In: Linear and Multilinear Algebra, Vol. 67, No. 6, 03.06.2019, p. 1074-1102.

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

Harvard

Kaygorodov, I, Pozhidaev, A & Saraiva, P 2019, 'On a ternary generalization of Jordan algebras', Linear and Multilinear Algebra, vol. 67, no. 6, pp. 1074-1102. https://doi.org/10.1080/03081087.2018.1443426

APA

Kaygorodov, I., Pozhidaev, A., & Saraiva, P. (2019). On a ternary generalization of Jordan algebras. Linear and Multilinear Algebra, 67(6), 1074-1102. https://doi.org/10.1080/03081087.2018.1443426

Vancouver

Kaygorodov I, Pozhidaev A, Saraiva P. On a ternary generalization of Jordan algebras. Linear and Multilinear Algebra. 2019 Jun 3;67(6):1074-1102. doi: 10.1080/03081087.2018.1443426

Author

Kaygorodov, Ivan ; Pozhidaev, Alexander ; Saraiva, Paulo. / On a ternary generalization of Jordan algebras. In: Linear and Multilinear Algebra. 2019 ; Vol. 67, No. 6. pp. 1074-1102.

BibTeX

@article{68a5076927e94049aa4c5ec115dd6d8f,

title = "On a ternary generalization of Jordan algebras",

abstract = "Based on the relation between the notions of Lie triple systems and Jordan algebras, we introduce the n-ary Jordan algebras, an n-ary generalization of Jordan algebras obtained via the generalization of the following property (R x , R y )∈ Der(A) where A is an n-ary algebra. Next, we study a ternary example of these algebras. Finally, based on the construction of a family of ternary algebras defined by means of the Cayley–Dickson algebras, we present an example of a ternary D x,y -derivation algebra (n-ary D x,y -derivation algebras are the non-commutative version of n-ary Jordan algebras). ",

keywords = "Cayley–Dickson construction, derivations, generalized Lie algebras, Jordan algebras, Lie triple systems, n-ary algebras, non-commutative Jordan algebras, TKK construction, 17C50, 17A42, IDENTITIES, LIE, Cayley-Dickson construction",

author = "Ivan Kaygorodov and Alexander Pozhidaev and Paulo Saraiva",

note = "Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2019",

month = jun,

day = "3",

doi = "10.1080/03081087.2018.1443426",

language = "English",

volume = "67",

pages = "1074--1102",

journal = "Linear and Multilinear Algebra",

issn = "0308-1087",

publisher = "Taylor and Francis Ltd.",

number = "6",

}

RIS

TY - JOUR

T1 - On a ternary generalization of Jordan algebras

AU - Kaygorodov, Ivan

AU - Pozhidaev, Alexander

AU - Saraiva, Paulo

PY - 2019/6/3

Y1 - 2019/6/3

N2 - Based on the relation between the notions of Lie triple systems and Jordan algebras, we introduce the n-ary Jordan algebras, an n-ary generalization of Jordan algebras obtained via the generalization of the following property (R x , R y )∈ Der(A) where A is an n-ary algebra. Next, we study a ternary example of these algebras. Finally, based on the construction of a family of ternary algebras defined by means of the Cayley–Dickson algebras, we present an example of a ternary D x,y -derivation algebra (n-ary D x,y -derivation algebras are the non-commutative version of n-ary Jordan algebras).

AB - Based on the relation between the notions of Lie triple systems and Jordan algebras, we introduce the n-ary Jordan algebras, an n-ary generalization of Jordan algebras obtained via the generalization of the following property (R x , R y )∈ Der(A) where A is an n-ary algebra. Next, we study a ternary example of these algebras. Finally, based on the construction of a family of ternary algebras defined by means of the Cayley–Dickson algebras, we present an example of a ternary D x,y -derivation algebra (n-ary D x,y -derivation algebras are the non-commutative version of n-ary Jordan algebras).

KW - Cayley–Dickson construction

KW - derivations

KW - generalized Lie algebras

KW - Jordan algebras

KW - Lie triple systems

KW - n-ary algebras

KW - non-commutative Jordan algebras

KW - TKK construction

KW - 17C50

KW - 17A42

KW - IDENTITIES

KW - LIE

KW - Cayley-Dickson construction

UR - http://www.scopus.com/inward/record.url?scp=85042939476&partnerID=8YFLogxK

U2 - 10.1080/03081087.2018.1443426

DO - 10.1080/03081087.2018.1443426

M3 - Article

AN - SCOPUS:85042939476

VL - 67

SP - 1074

EP - 1102

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 6

ER -

ID: 12079194