Leibniz 2-Algebras and Twisted Courant Algebroids

REFERENCES

• Ammar , M. , Poncin , N. ( 2010 ). Coalgebraic approach to the loday infinity category, stem differential for 2n-ary graded and homotopy algebras . Ann. Inst. Fourier (Grenoble) 60 ( 1 ): 355 – 387 .
   Web of Science ®Google Scholar
• Armstrong , S. Note on pre-Courant algebroid structures for parabolic geometries. arXiv:0709.0919v3.
   Google Scholar
• Baez , J. , Crans , A. S. ( 2004 ). Higher-dimensional algebra VI: Lie 2-algebras . Theory & Appl. Categ. 12 : 492 – 528 .
   Google Scholar
• Baez , J. , Rogers , C. ( 2010 ). Categorified symplectic geometry and the string Lie 2-algebra . Homology, Homotopy & Applications 12 : 221 – 236 .
   Web of Science ®Google Scholar
• Bressler , P. ( 2007 ). The first Pontryagin class . Compos. Math. 143 ( 5 ): 1127 – 1163 .
   Web of Science ®Google Scholar
• Carey , A. , Murray , M. , Wang , B. L. Higher bundle gerbes and cohomology classes in gauge theories. arXiv:hep-th/9511169.
   Google Scholar
• Casas , J. M. , Khmaladze , E. , Ladra , M. ( 2008 ). Crossed modules for Leibniz n-algebras . Forum Math. 20 : 841 – 858 .
   Web of Science ®Google Scholar
• Cattaneo , A. S. , Xu , P. ( 2004 ). Integration of twisted Poisson structures . J. Geom. Phys. 49 : 187 – 196 .
   Web of Science ®Google Scholar
• Chen , Z. , Stienon , M. , Xu , P. ( 2013 ). On regular Courant algebroids . J. Symplectic Geom. 11 ( 1 ): 1 – 24 .
   Web of Science ®Google Scholar
• Grützmann , M. ( 2011 ). H-twisted Lie algebroids . J. Geom. Phys. 61 : 476 – 484 .
   Web of Science ®Google Scholar
• Grützmann , M. H-Twisted Courant Algebroids. arXiv:1101.0993.
   Google Scholar
• Gualtieri , M. ( 2003 ). Generalized Complex Geometry. Ph.D. thesis. St John's College, University of Oxford .
   Google Scholar
• Hansen , M. , Strobl , T. ( 2010 ). First class constrained systems and twisting of courant algebroids by a closed 4-form. Fundamental Interactions. Hackensack, NJ: World Scientific, pp. 115–144 .
   Google Scholar
• Hull , C. M. ( 2007 ). Generalised geometry for M-theory . J. High Energy Phys. 7 : 079 .
   Web of Science ®Google Scholar
• Lada , T. , Stasheff , J. ( 1993 ). Introduction to sh Lie algebras for physicists . Int. Jour. Theor. Phys. 32 ( 7 ): 1087 – 1103 .
   Web of Science ®Google Scholar
• Liu , Z.-J. , Weinstein , A. , Xu , P. ( 1997 ). Manin triples for Lie bialgebroids . J. Diff. Geom. 45 : 547 – 574 .
   Web of Science ®Google Scholar
• Loday , J.-L. ( 1993 ). Une version non commutative des algèbres de Lie: Les algèbres de Leibniz . Enseign. Math. 39 ( 2 ): 269 – 293 .
   Google Scholar
• Loday , J.-L. , Pirashvili , T. ( 1993 ). Universal enveloping algebras of Leibniz algebras and (co)homology . Math. Ann. 296 : 139 – 158 .
   Web of Science ®Google Scholar
• Petalidou , F. ( 2007 ). On the geometric quantization of twisted Poisson manifolds . J. Math. Phys. 48 : 083502 .
   Web of Science ®Google Scholar
• Rogers , C. (2012). L ∞-algebras from multisymplectic geometry. Lett. Math. Phys. 100(1):29–50.
   Web of Science ®Google Scholar
• Roytenberg , D. ( 1998 ). Courant algebroids and strongly homotopy Lie algebras . Lett. Math. Phys. 46 ( 1 ): 81 – 93 .
   Web of Science ®Google Scholar
• Roytenberg , D. ( 1999 ). Courant algebroids, derived brackets and even symplectic supermanifolds. Ph.D. thesis. UC Berkeley. arXiv:math.DG/9910078 .
   Google Scholar
• Roytenberg , D. ( 2007 ). On weak Lie 2-algebras. In: XXVI Workshop on Geometrical Methods in Physics, Volume 956 of AIP Conf. Proc. Melville, NY: Amer. Inst. Phys., pp. 180–198 .
   Google Scholar
• Schlessinger , M. , Stasheff , J. ( 1985 ). The Lie algebra structure of tangent cohomology and deformation theory . J. Pure Appl. Algebra 38 : 313 – 322 .
   Web of Science ®Google Scholar
• Ševera , P. , Weinstein , A. ( 2001 ). Poisson geometry with a 3-form background . Prog. Theor. Phys. Suppl. 144 : 145 – 154 .
   Google Scholar
• Sheng , Y. , Liu , Z.-J. , Zhu , C. ( 2011 ). Omni-Lie 2-algebras and their Dirac structures . J. Geom. Phys. 61 : 560 – 575 .
   Web of Science ®Google Scholar
• Sheng , Y. , Zhu , C. ( 2011 ). Semidirect products of representations up to homotopy . Pacific J. Math. 249 ( 1 ): 211 – 236 .
   Web of Science ®Google Scholar
• Sheng , Y. , Zhu , C. ( 2012 ). Integration of semidirect product Lie 2-algebras . Int. J. Geom. Methods Mod. Phys. 9 ( 5 ): 1250043 .
   Web of Science ®Google Scholar
• Uchino , K. ( 2011 ). Derived brackets and sh Leibniz algebras . J. Pure Appl. Algebra 215 : 1102 – 1111 .
   Web of Science ®Google Scholar
• Vaisman , I. ( 2005 ). Transitive Courant algebroids . Int. J. Math. Math. Sci. 11 : 1737 – 1758 .
   Google Scholar
• Zambon , M. ( 2012 ). L ∞-algebras and higher analogues of Dirac structures and Courant algebroids . J. Symp. Geom. 10 ( 4 ): 563 – 599 .
   Web of Science ®Google Scholar
• Communicated by A. Elduque.
   Google Scholar