On Identities of a Ternary Quaternion Algebra

Beites, Patrícia Damas; Nicolás, Alejandro; Pozhidaev, A. P.; Saraiva, Paulo

doi:10.1080/00927871003601659

Cited by 4 publications

(5 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…defined on the ternary Filippov algebra A 1 with anticommutative multiplication [., ., .] (see [1]). Indeed, being {x, y, z} (+) = sym ({x, y, z})…”

Section: Another Example Of a Simple Ternary Jordan Algebramentioning

confidence: 96%

“…Recall now that an identity satisfied by a ternary algebra is said to be of degree (or level) k, with k ∈ N, if k is the number of times that the multiplication appears in each term of the identity (see [1]). Next, we are going to study the identities of degrees 1 and 2, respectively, valid in the ternary Jordan algebra A.…”

Section: Another Example Of a Simple Ternary Jordan Algebramentioning

confidence: 99%

See 1 more Smart Citation

On a ternary generalization of Jordan algebras

Kaygorodov,

Pozhidaev,

Saraiva

2017

Preprint

View full text Add to dashboard Cite

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).

show abstract

“…defined on the ternary Filippov algebra A 1 with anticommutative multiplication [., ., .] (see [1]). Indeed, being {x, y, z} (+) = sym ({x, y, z})…”

Section: Another Example Of a Simple Ternary Jordan Algebramentioning

confidence: 96%

Section: Another Example Of a Simple Ternary Jordan Algebramentioning

confidence: 99%

On a ternary generalization of Jordan algebras

Kaygorodov,

Pozhidaev,

Saraiva

2017

Preprint

View full text Add to dashboard Cite

show abstract

“…As far as level 3 is concerned, we use the random vectors method to answer a question posed in [2], that is, we conclude that there are no new level 3 identities of A. See, for instance, the work [3] of Bremner and Hentzel for more details about the latter method.…”

Section: Beites and Nicolásmentioning

confidence: 98%

“…We recall, in Section 5, the levels 1 and 2 identities of A obtained in [2] mainly through the matrix expansion method. As far as level 3 is concerned, we use the random vectors method to answer a question posed in [2], that is, we conclude that there are no new level 3 identities of A.…”

Section: Beites and Nicolásmentioning

confidence: 99%

See 1 more Smart Citation

An Associative Triple System of the Second Kind

Beites

Nicolás

2016

Communications in Algebra

Self Cite

View full text Add to dashboard Cite

We study the associative triple system of the second kind A obtained from a new multiplication defined in the underlying vector space of the four-dimensional ternary Filippov algebra A 4 . Descriptions of the automorphisms group and the antiautomorphisms set of A, both constituted by certain orthogonal matrices, are presented. Through a Leibniz-type formula for a power of a derivation of A, the link between the mentioned group and the Lie algebra of derivations of A is established. Applying the random vectors method, which involves computational linear algebra on matrices, level 3 identities of A are determined. Moreover, levels 1 and 2 identities of certain reduced algebras that are composition algebras, some Hurwitz too and others isomorphic to standard composition algebras, are also calculated.

show abstract