Deligne's conjecture on Hochschild cohomology
In deformation theory, a branch of mathematics, Deligne's conjecture is about the operadic structure on Hochschild cochain complex. Various proofs have been suggested by Dmitry Tamarkin,[1][2] Alexander A. Voronov,[3] James E. McClure and Jeffrey H. Smith,[4] Maxim Kontsevich and Yan Soibelman,[5] and others, after an initial input of construction of homotopy algebraic structures on the Hochschild complex.[6][7] It is of importance in relation with string theory.
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References[edit]
- ^ Tamarkin, Dmitry E. (1998). "Another proof of M. Kontsevich formality theorem". arXiv:math/9803025.
- ^ Hinich, Vladimir (2003). "Tamarkin's proof of Kontsevich formality theorem". Forum Math. 15 (4): 591–614. arXiv:math/0003052. doi:10.1515/form.2003.032. S2CID 220814.
- ^ Voronov, Alexander A. (2000). "Conférence Moshé Flato 1999". Conférence Moshé Flato 1999, Vol. II (Dijon). Dordrecht: Kluwer Acad. Publ. pp. 307–331. arXiv:math/9908040. doi:10.1007/978-94-015-1276-3_23. ISBN 978-90-481-5551-4.
- ^ McClure, James E.; Smith, Jeffrey H. (2002). "A solution of Deligne's Hochschild cohomology conjecture". Recent progress in homotopy theory (Baltimore, MD, 2000). Providence, RI: Amer. Math. Soc. pp. 153–193. arXiv:math/9910126.
- ^ Kontsevich, Maxim; Soibelman, Yan (2000). "Deformations of algebras over operads and the Deligne conjecture". Conférence Moshé Flato 1999, Vol. I (Dijon). Dordrecht: Kluwer Acad. Publ. pp. 255–307. arXiv:math/0001151.
- ^ Getzler, Ezra; Jones, J. D. S. (1994). "Operads, homotopy algebra and iterated integrals for double loop spaces". arXiv:hep-th/9403055.
- ^ Voronov, A. A.; Gerstenhaber, M. (1995). "Higher operations on the Hochschild complex". Funct. Anal. Its Appl. 29: 1–5. doi:10.1007/BF01077036. S2CID 121740728.