Associator dependent algebras and Koszul duality

Dotsenko, Vladimir; Bremner, Murray R.

doi:10.1007/s10231-022-01278-8

Annali di Matematica

2022

DOI: 10.1007/s10231-022-01278-8

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Associator dependent algebras and Koszul duality

Vladimir Dotsenko

Murray R. Bremner

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2023

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Sectional nonassociativity of metrized algebras

Fox

2023

Annali di Matematica

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The sectional nonassociativity of a metrized (not necessarily associative or unital) algebra is defined analogously to the sectional curvature of a pseudo-Riemannian metric, with the associator in place of the Levi-Civita covariant derivative. For commutative real algebras nonnegative sectional nonassociativity is usually called the Norton inequality, while a sharp upper bound on the sectional nonassociativity of the Jordan algebra of Hermitian matrices over a real Hurwitz algebra is closely related to the Böttcher–Wenzel-Chern-do Carmo-Kobayashi inequality. These and other basic examples are explained, and there are described some consequences of bounds on sectional nonassociativity for commutative algebras. A technical point of interest is that the results work over the octonions as well as the associative Hurwitz algebras.

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Sectional nonassociativity of metrized algebras

Fox

2023

Annali di Matematica

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Associator dependent algebras and Koszul duality

Cited by 1 publication

References 30 publications

Sectional nonassociativity of metrized algebras

Sectional nonassociativity of metrized algebras

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