Courant brackets on noncommutative algebras and omni-Lie algebras
Kyousuke Uchino
math.SGarXiv:math/0604101
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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