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November 2014 Dirac Lie Groups
David Li-Bland, Eckhard Meinrenken
Asian J. Math. 18(5): 779-816 (November 2014).

Abstract

A classical theorem of Drinfel'd states that the category of simply connected Poisson Lie groups $H$ is isomorphic to the category of Manin triples $(\mathfrak{d, g, h})$, where $\mathfrak{h}$ is the Lie algebra of $H$. In this paper, we consider Dirac Lie groups, that is, Lie groups $H$ endowed with a multiplicative Courant algebroid $A$ and a Dirac structure $E \subseteq \mathbb{A}$ for which the multiplication is a Dirac morphism. It turns out that the simply connected Dirac Lie groups are classified by so-called Dirac Manin triples. We give an explicit construction of the Dirac Lie group structure defined by a Dirac Manin triple, and develop its basic properties.

Citation

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David Li-Bland. Eckhard Meinrenken. "Dirac Lie Groups." Asian J. Math. 18 (5) 779 - 816, November 2014.

Information

Published: November 2014
First available in Project Euclid: 2 December 2014

zbMATH: 1320.53102
MathSciNet: MR3287003

Subjects:
Primary: 53D17
Secondary: 17B62, 53D20

Rights: Copyright © 2014 International Press of Boston

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Vol.18 • No. 5 • November 2014
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