Klimčík, C.; Strobl, T. WZW-Poisson manifolds. (English) Zbl 1027.70023 J. Geom. Phys. 43, No. 4, 341-344 (2002). Summary: We observe that a term of WZW-type can be added to the Lagrangian of Poisson \(\sigma\)-model in such a way that the algebra of first-class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting WZW-Poisson manifold \(M\) is characterized by a bivector \(\Pi\) and by a closed three-form \(H\) such that \(1/2[\Pi,\Pi]_S= \langle H,\pi \otimes \Pi \otimes \Pi \rangle\), the symbol \([\cdot,\cdot]_S\) denotes the Schouten bracket. Cited in 2 ReviewsCited in 66 Documents MSC: 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics 53D17 Poisson manifolds; Poisson groupoids and algebroids Keywords:twisted Poisson manifold; Dirac structures; controlled nonassociativity; Poisson sigma-model; Lagrangian; first-class constraints; WZW-Poisson manifold × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Witten, E., Nonabelian bosonization in two dimensions, Commun. Math. Phys., 92, 455 (1984) · Zbl 0536.58012 [2] P. Schaller, T. Strobl, Introduction to Poisson \(σ\) hep-th/9507020; P. Schaller, T. Strobl, Introduction to Poisson \(σ\) hep-th/9507020 · Zbl 1015.81574 [3] T. Strobl, in preparation.; T. Strobl, in preparation. [4] Klimčı́k, C.; Ševera, P., Open strings and D-branes in WZNW model, Nucl. Phys. B, 488, 653 (1997) · Zbl 0925.81240 [5] Ikeda, N., Two-dimensional gravity and nonlinear gauge theory, Ann. Phys., 235, 435 (1994) · Zbl 0807.53070 [6] Alekseev, A.; Schaller, P.; Strobl, T., The topological G/G WZW model in the generalized momentum representation, Phys. Rev. D, 52, 7146 (1995) [7] A. Alekseev, Y. Kosmann-Schwarzbach, E. Meinrenken, Quasi-Poisson manifolds, Math.DG/0006168.; A. Alekseev, Y. Kosmann-Schwarzbach, E. Meinrenken, Quasi-Poisson manifolds, Math.DG/0006168. · Zbl 1006.53072 [8] Courant, T., Dirac manifolds, Trans. AMS, 319, 631 (1990) · Zbl 0850.70212 [9] L. Cornalba, R. Schiappa, Nonassociative star product deformations for D-brane worldvolumes in curved backgrounds. hep-th/0101219; L. Cornalba, R. Schiappa, Nonassociative star product deformations for D-brane worldvolumes in curved backgrounds. hep-th/0101219 · Zbl 1042.81065 [10] C.M. Hofman, W.K. Ma, Deformations of closed strings and topological open membranes. hep-th/0102201; C.M. Hofman, W.K. Ma, Deformations of closed strings and topological open membranes. hep-th/0102201 [11] J.-S. Park, Topological open p-branes. hep-th/0012141; J.-S. Park, Topological open p-branes. hep-th/0012141 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.