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Courant brackets on noncommutative algebras and omni-Lie algebras

Kyousuke Uchino
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Abstract

We define a Courant bracket on an associative algebra using the theory of Hochschild homology, and we introduce the notion of Dirac algebra. We show that the bracket of an omni-Lie algebra is quite a kind of Courant bracket.

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Kyousuke Uchino. 2006-04-05. Courant brackets on noncommutative algebras and omni-Lie algebras. https://arxiv.org/abs/math/0604101

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