Deligne's conjecture on Hochschild cohomology

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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.

See also

References

  1. ↑ Tamarkin, Dmitry E. (1998). "Another proof of M. Kontsevich formality theorem". arXiv:math/9803025.
  2. ↑ Hinich, Vladimir (2003). "Tamarkin's proof of Kontsevich formality theorem". Forum Math. 15 (4): 591–614. doi:10.1515/form.2003.032. https://www.degruyter.com/view/journals/form/15/4/article-p591.xml. 
  3. ↑ Voronov, Alexander A. (2000). "Conférence Moshé Flato 1999". Dordrecht: Kluwer Acad. Publ.. pp. 307–331. doi:10.1007/978-94-015-1276-3_23. ISBN 978-90-481-5551-4. 
  4. ↑ McClure, James E.; Smith, Jeffrey H. (2002). "A solution of Deligne's Hochschild cohomology conjecture". Providence, RI: Amer. Math. Soc.. pp. 153–193. http://www.ams.org.ezp2.lib.umn.edu/books/conm/293/. 
  5. ↑ Kontsevich, Maxim; Soibelman, Yan (2000). "Deformations of algebras over operads and the Deligne conjecture". Dordrecht: Kluwer Acad. Publ.. pp. 255–307. 
  6. ↑ Getzler, Ezra; Jones, J. D. S. (1994). "Operads, homotopy algebra and iterated integrals for double loop spaces". arXiv:hep-th/9403055.
  7. ↑ Voronov, A. A.; Gerstenhaber, M. (1995). "Higher operations on the Hochschild complex". Funct. Anal. Its Appl. 29: 1–5. doi:10.1007/BF01077036. https://link.springer.com/article/10.1007%2FBF01077036. 

Further reading



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