Higher Courant-Dorfman algebras and associated higher Poisson vertex algebras

[1] Ted Courant.: Dirac manifolds, Transactions of the American Mathematical

Society Vol. 319, No. 2 (Jun., 1990), pp. 631-661

[2] Marco Gualtieri.: Generalized complex geometry and T-duality,arxiv:0401221

[3] V. G. Drinfel’d.: Hamiltonian structures on Lie groups, Lie bialgebras and

the geometric meaning of classical Yang-Baxter equations Dokl. Akad. Nauk

SSSR 268.2 (1983), pp. 285–287.

[4] Gil R. Cavalcanti, Marco Gualtieri.: Generalized complex geometry,A

Celebration of the Mathematical Legacy of Raoul Bott (CRM Proceedings and Lecture Notes), American Mathematical Society, 2010, pp. 341366.arxiv:1106.1747

[5] Dmitry Roytenberg.: AKSZ-BV Formalism and Courant Algebroid-induced

Topological Field Theories,Lett.Math.Phys.79:143-159,2007,arxiv:0608150

[6] A. Coimbra, C. Strickland-Constable and D. Waldram,: Supergravity as Generalised Geometry I: Type II Theories JHEP 1111 (2011) 091,arxiv:1107.1733

[7] Izu Vaisman.: Towards a double field theory on para-Hermitian manifolds,J.

Math. Phys. 54, 123507 (2013) arxiv:1209.0152

[8] Dmitry Roytenberg.: Courant-Dorfman algebras and their cohomology,Lett.

Math. Phys. (2009) 90:311-351, arxiv:0902.4862

[9] Dmitry Roytenberg.: On the structure of graded symplectic supermanifolds

and Courant algebroids, Contemp. Math., Vol. 315, Amer. Math. Soc., Providence, RI, 2002, arxiv:0203110

[10] Zhang-Ju Liu, Alan Weinstein, Ping Xu.: Manin Triples for Lie Bialgebroids,J. Diff. Geom., 45:547-574 arxiv:9508013

[11] V. G. Knizhnik and A. B. Zamolodchikov.: Current algebra and Wess-Zumino

model in two dimensions, Nucl.Phys.B 247 (1984) 83-103

[12] Victor G. Kac; Vertex algebras for beginners, Lecture Ser., vol 10, AMS, 1996.

Second edition, 1998

[13] Victor Kac.: Introduction to vertex algebras, Poisson vertex algebras, and

integrable Hamiltonian PDE , arxiv:1512.00821

38

[14] Reimundo Heluani, Victor G. Kac:

Supersymmetric vertex algebras,Commun.Math.Phys.271:103-178,2007 arxiv:0603633

[15] Aliaa Barakat, Alberto De Sole, Victor G. Kac.: Poisson vertex algebras in

the theory of Hamiltonian equations,Jpn. J. Math. 4 (2009), no. 2, 141-252

arxiv:0907.1275

[16] Pedram Hekmati, Varghese Mathai.: T-duality of current algebras and their

quantization,Contemporary Mathematics, 584 (2012) 17-38 arxiv:1203.1709

[17] Luis Alvarez-C´

onsul, David Fern´andez, Reimundo Heluani.: Noncommutative

Poisson vertex algebras and Courant-Dorfman algebras, arxiv:2106.00270

[18] Giulio Bonelli, Maxim Zabzine.: From current algebras for p-branes to topological M-theory,JHEP 0509 (2005) 015 arxiv:0507051

[19] Machiko Hatsuda, Tetsuji Kimura.: Canonical approach to Courant brackets

for D-branes,Journal of High Energy Physics 34 (2012) arxiv:1203.5499

[20] Alberto S. Cattaneo, Florian Schaetz.:

arxiv:1011.3401

Introduction to supergeometry,

[21] Jian Qiu, Maxim Zabzine.: Introduction to Graded Geometry, BatalinVilkovisky Formalism and their Applications, arxiv:1105.2680

[22] I. A. Batalin, G. A. Vilkovisky,: Gauge algebra and quantization, Phys. Lett.,

102B:27, 1981

[23] I. A. Batalin and G. A. Vilkovisky,: Relativistic S-matrix of dynamical systems

with boson and fermion constraints, Phys. Lett. B 69 (1977), 309–312

[24] I. A. Batalin and E. S. Fradkin,: A generalized canonical formalism and quantization of reducible gauge theories, Phys. Lett. B 122, 157–164 (1983)

[25] Anton Alekseev, Thomas Strobl.: Current Algebras and Differential Geometry,JHEP 0503 (2005) 035 arxiv:0410183

[26] Joel Ekstrand, Maxim Zabzine.: Courant-like brackets and loop spaces,JHEP

1103:074,2011 arxiv:0903.3215

[27] Frank Keller, Stefan Waldmann.: Deformation theory of Courant algebroids via the Rothstein algebra,Journal of Pure and Applied Algebra 219(8)

arxiv:0807.0584

[28] G. Bonavolonta, N. Poncin; On the category of Lie n-algebroids, J. Geom.

Phys., 73 (2013), 70-90 arxiv:1207.3590

[29] Theodore Voronov.: Higher derived brackets and homotopy algebras,J. Pure

and Appl. Algebra. 202 (2005), Issues 1-3, 1 November 2005, 133-153

arxiv:0304038

39

[30] Joel Ekstrand: Going round in circles From sigma models to vertex algebras

and back , Doctoral thesis,2011.

[31] Noriaki Ikeda, Kozo Koizumi.:

Current Algebras and QP Manifolds,International Journal of Geometric Methods in Modern Physics 10(6)

arxiv:1108.0473

[32] Noriaki Ikeda, Xiaomeng Xu.: Current Algebras from DG Symplectic Pairs

in Supergeometry, arxiv:1308.0100

[33] Taiki Bessho, Marc A. Heller, Noriaki Ikeda, Satoshi Watamura: Topological

Membranes, Current Algebras and H-flux - R-flux Duality based on Courant

Algebroids, J. High Energ. Phys. 2016, 170 (2016). arxiv:1511.03425

[34] Alex S. Arvanitakis.: Brane current algebras and generalised geometry from

QP manifolds, J. High Energ. Phys. 2021, 114 (2021). arxiv:2103.08608

[35] M.A. Grigoriev, A.M. Semikhatov, I.Yu. Tipunin.: BRST Formalism and

Zero Locus Reduction,J.Math.Phys. 42 (2001) 3315-3333 arxiv:0001081

[36] A.Yu.Alekseev, P.Schaller, T.Strobl.: The Topological G/G WZW Model in

the Generalized Momentum Representation,Phys.Rev. D52 (1995) 7146-7160

arxiv:9505012

[37] Noriaki Ikeda.:

Lectures on AKSZ Sigma Models for PhysicistsNoncommutative Geometry and Physics 4, Workshop on Strings,

Membranes and Topological Field Theory: 79-169, 2017, World scientific,

Singapore, arxiv:1204.3714

40

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