Nonassociative Coefficient Algebras for Steinberg Unitary Lie Algebras

Allison, Bruce; Faulkner, John R.

doi:10.1006/jabr.1993.1202

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Introduction4

(~Y) = -(=Y) (D(~))~-d(b('dz))+d((ca)b)-(dc)(ab)+b((c1

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Cited by 52 publications

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“…Later on, a quite general construction was given by Allison and Faulkner [2] of Lie algebras out of structurable ones. In the particular case of the tensor product of two unital composition algebras, this construction provides another symmetric construction of Freudenthal's Magic Square.…”

Section: Introductionmentioning

confidence: 99%

The Magic Square and Symmetric Compositions II

Elduque¹

2007

Rev. Mat. Iberoam.

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The construction of Freudenthal's Magic Square, which contains the exceptional simple Lie algebras of types F 4 , E 6 , E 7 and E 8 , in terms of symmetric composition algebras is further developed here. The para-Hurwitz algebras, which form a subclass of the symmetric composition algebras, will be defined, in the split case, in terms of the natural two dimensional module for the simple Lie algebra sl 2 . As a consequence, it will be shown how all the Lie algebras in Freudenthal's Magic Square can be constructed, in a unified way, using copies of sl 2 and of its natural module.

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Section: Introductionmentioning

confidence: 99%

The Magic Square and Symmetric Compositions II

Elduque¹

2007

Rev. Mat. Iberoam.

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“…Recently, these approaches have been interpreted by Barton and Sudbery [3,4] as a construction depending on two composition algebras and closely related to the triality principle. A similar construction has been given by Landsberg and Manivel [14,15], inspired by previous work of Allison and Faulkner [2].…”

Section: Introductionmentioning

confidence: 87%

The Magic Square and Symmetric Compositions

Elduque¹

2004

Rev. Mat. Iberoam.

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“…Identity (4) follows from (1) ff we apply involution to both sides of the latter. Identity (5) was proved in [6]. Let (A,-) be a structurable algebra.…”

Section: (~Y) = -(=Y) (D(~))~-d(b('dz))+d((ca)b)-(dc)(ab)+b((cmentioning

confidence: 96%

Structurable coalgebras

Zhelyabin¹

1996

Algebr Logic

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Nonassociative Coefficient Algebras for Steinberg Unitary Lie Algebras

Cited by 52 publications

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The Magic Square and Symmetric Compositions II

The Magic Square and Symmetric Compositions II

The Magic Square and Symmetric Compositions

Structurable coalgebras

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