Split spin factor algebras

McInroy, Justin; Shpectorov, Sergey

doi:10.1016/j.jalgebra.2021.12.022

Cited by 7 publications

(3 citation statements)

References 7 publications

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“…This proves (38). Furthermore, since L c 1 is non-degenerated linear endomorphism, we also deduce that 0 (40) implies (39).…”

Section: 2supporting

confidence: 60%

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Medial and isospectral algebras

Krasnov¹,

Tkachev²

2022

Preprint

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The purpose of this paper is to give a systematic study of two new classes of commutative nonassociative algebras, the so-called isospectral and medial algebras. An isospectral algebra A is a generic commutative nonassociative algebra whose idempotents have the same Peirce spectrum. A medial algebra is algebra with identity (xy)(zw) = (xz)(yw). We show that these two classes are essentially coincide. We also prove that any medial spectral algebra is isomorphic to a certain isotopic deformation of the commutative associative quotient algebra K[z]/(z n − 1).Medial magma, Isospectral algebras, Quasigroups, Idempotents, Peirce decomposition

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“…This proves (38). Furthermore, since L c 1 is non-degenerated linear endomorphism, we also deduce that 0 (40) implies (39).…”

Section: 2supporting

confidence: 60%

“…Remark 5.6. Combining the latter with the property that any idempotent has the same spectrum and fusion rules, one concludes that an isospectral algebra is axial in the sense of definitions in [24], [46], [33], [39]. The axes in the present context are all idempotents of A.…”

Section: Isospectral Algebrasmentioning

confidence: 63%

Medial and isospectral algebras

Krasnov¹,

Tkachev²

2022

Preprint

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“…Axial algebras are a recent class of non-associative commutative algebras introduced by Hall, Rehren and Shpectorov [18] in 2015. They can be seen as a certain generalisation of commutative, associative algebras, and as a common frame for Majorana algebras [18,39], Jordan algebras [19,20,28] and other types of algebras appearing in mathematical physics. They are also related to code algebras [7].…”

Section: Introductionmentioning

confidence: 99%

Central extensions of axial algebras

Kaygorodov¹,

González²,

Páez-Guillán³

2022

Preprint

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In this article, we develop a further adaptation of the method of Skjelbred-Sund to construct central extensions of axial algebras. We use our method to prove that all axial central extensions (with respect to a maximal set of axes) of complex simple finite-dimensional Jordan algebras are split, and that all non-split axial central extensions of dimension n ≤ 4 over an algebraically closed field of characteristic not 2 are Jordan. Also, we give a classification of 2-dimensional axial algebras and describe some important properties of these algebras.

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From forbidden configurations to a classification of some axial algebras of Monster type

McInroy

Shpectorov

2023

Journal of Algebra

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Split spin factor algebras

Cited by 7 publications

References 7 publications

Medial and isospectral algebras

Medial and isospectral algebras

Central extensions of axial algebras

From forbidden configurations to a classification of some axial algebras of Monster type

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