Vertex algebroids à la Beilinson-Drinfeld
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 2-3, pp. 205-234.

Ces notes informelles sont une introduction aux algébroïdes vertex en suivant les lignes suggérées par Beilinson et Drinfeld.

These informal notes are an introduction to vertex algebroids along the lines suggested by Beilinson and Drinfeld.

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     author = {Malikov, Fyodor},
     title = {Vertex algebroids \`a la {Beilinson-Drinfeld}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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Malikov, Fyodor. Vertex algebroids à la Beilinson-Drinfeld. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 2-3, pp. 205-234. doi : 10.5802/afst.1494. http://archive.numdam.org/articles/10.5802/afst.1494/

[1] Arakawa (T.), Chebotarov (D.), Malikov (F.).— ‘Algebras of twisted chiral differential operators and affine localization of g-modules”, Selecta Math. New Series, Vol. 17 Issue 1, p. 1-46 (2011). | Article | MR 2764998 | Zbl 1233.17021

[2] Arakawa (T.), Malikov (F.).— “A chiral Borel-Weil-Bott theorem”, Adv. in Math. Vol. 229, Issue 5, p. 2908-2949 (2012). | Article | MR 2889151

[3] Arkhipov (S.), Gaitsgory (D.).— Differential operators on the loop group via chiral algebras,Int. Math. Res. Not. no. 4, p. 165-210 (2002). | Article | Zbl 0997.17016

[4] Bakalov (B.), Kac (V.G.), Voronov (A.A.).— Cohomology of conformal algebras. Comm. Math. Phys., 200 (1999), pp. 561-598. | Article | MR 1675121 | Zbl 0959.17018

[5] Beilinson (A.), Drinfeld (V.).— Chiral algebras. American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004. vi+375 pp. ISBN : 0-8218-3528-9 | Article

[6] Borel (A.) et al..— Algebraic D-modules Academic Press, Inc. (1987).

[7] Borcherds (R.E.).— « Vertex algebras, Kac-Moody algebras, and the Monster. » Proceedings of the National Academy of Sciences 83.10 p. 3068-3071 (1986). | Article | MR 843307 | Zbl 0613.17012

[8] Frenkel (E.), Ben-Zvi (D.).— Vertex algebras and algebraic curves. Second edition. Mathematical Surveys and Monographs, 88. American Mathematical Society, Providence, RI (2004). | Article | Zbl 1106.17035

[9] Gorbounov (V.), Malikov (F.), Schechtman (V.).— Gerbes of chiral differential operators. II. Vertex algebroids, Invent. Math. 155., no. 3, p. 605-680 (2004). | Article | MR 2038198 | Zbl 1056.17022

[10] Heluani (R.).— Supersymmetry of the chiral de Rham complex. II. Commuting sectors, Int. Math. Res. Not. 2009, no. 6, p. 953-987. | Article | MR 2487489 | Zbl 1164.81014

[11] Hinich (V.).— unpublished manuscript.

[12] Huang (Yi.-Z.), Lepowski (J.).— On the D-module and formal variable approach to vertex operator algebras, in : Topics in geometry, p.175-202, Birkhäuser, Boston (1996). | Article

[13] Kac (V.).— Vertex algebras for beginners. University Lecture Series, 10. American Mathematical Society, Providence, RI (1997). viii+141 pp. ISBN : 0-8218-0643-2 | Article | MR 1651389 | Zbl 0861.17017

[14] Lada (T.), Markl (M.).— Strongly homotopy Lie algebras, Comm. in Algebra Vol. 23, Issue 6, p. 2147-2161 (1995). | Article | MR 1327129 | Zbl 0999.17019

[15] Linshaw (A.), Mathai (V.).— Twisted chiral de Rham complex, generalized geometry, and T-duality, posted on : arXiv :1412.0166 | Article | MR 3370615 | Zbl 1351.53101

[16] Lada (T.) and Stasheff (J.).— Introduction to sh Lie algebras for physicists. International Journal of Theoretical Physics Vol. 32, No. 7, p. 1087-1103 (1993). | Article | MR 1235010 | Zbl 0824.17024

[17] Malikov (F.), Schechtman (V.), Vaintrob (A.).— Chiral de Rham complex, Comm. in Math. Phys. 204, p. 439-473 (1999). | Article | MR 1704283 | Zbl 0952.14013

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