Lie algebras graded by the root systems 𝐵𝐶ᵣ,𝑟≥2

Allison, Bruce; Benkart, Georgia; Gao, Yun

doi:10.1090/memo/0751

Cited by 33 publications

(76 citation statements)

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“…Our construction was inspired by several properties of J-ternary algebras; see Definition 3.6 and [ABG,3.12].…”

Section: A Coordinate-free Construction Of Quadrangular Algebrasmentioning

confidence: 99%

“…Assume that (v') holds, we have ABG,3.12]). Let J be a Jordan k-algebra and let X be a k-vector space with action • : J × X → X.…”

Section: Linearizing This Expression Gives Us (V')mentioning

confidence: 99%

“…In the following Lemma we consider the Peirce decomposition of special J-modules; see also [ABG,6.61].…”

Section: Linearizing This Expression Gives Us (V')mentioning

confidence: 99%

“…For example, consider [ABG,Example 6.81] with the zero skew hermitian form. Examples like this we clearly want to avoid.…”

Section: Remark 38 (I) We Show That For Allmentioning

confidence: 99%

“…Our construction relies in an essential way on the theory of J-ternary algebras and their Peirce decomposition, see [ABG,Sections 3.12 and 6.61].…”

Section: Introductionmentioning

confidence: 99%

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A new construction of Moufang quadrangles of type 𝐸₆,𝐸₇ and 𝐸₈

Boelaert

Medts

2014

Trans. Amer. Math. Soc.

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In the classification of Moufang polygons by J. Tits and R. Weiss, the most intricate case is by far the case of the exceptional Moufang quadrangles of type E 6 , E 7 and E 8 , and in fact, the construction that they present is ad-hoc and lacking a deeper explanation. We will show how tensor products of two composition algebras can be used to construct these Moufang quadrangles in characteristic different from 2.As a byproduct, we will obtain a method to construct any Moufang quadrangle in characteristic different from two from a module for a Jordan algebra.

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“…Our construction was inspired by several properties of J-ternary algebras; see Definition 3.6 and [ABG,3.12].…”

Section: A Coordinate-free Construction Of Quadrangular Algebrasmentioning

confidence: 99%

“…Assume that (v') holds, we have ABG,3.12]). Let J be a Jordan k-algebra and let X be a k-vector space with action • : J × X → X.…”

Section: Linearizing This Expression Gives Us (V')mentioning

confidence: 99%

“…In the following Lemma we consider the Peirce decomposition of special J-modules; see also [ABG,6.61].…”

Section: Linearizing This Expression Gives Us (V')mentioning

confidence: 99%

“…For example, consider [ABG,Example 6.81] with the zero skew hermitian form. Examples like this we clearly want to avoid.…”

Section: Remark 38 (I) We Show That For Allmentioning