An homotopy formula for the Hochschild cohomology

M. De Wilde; P. B. A. Lecomte

Compositio Mathematica (1995)

  • Volume: 96, Issue: 1, page 99-109
  • ISSN: 0010-437X

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De Wilde, M., and Lecomte, P. B. A.. "An homotopy formula for the Hochschild cohomology." Compositio Mathematica 96.1 (1995): 99-109. <http://eudml.org/doc/90358>.

@article{DeWilde1995,
author = {De Wilde, M., Lecomte, P. B. A.},
journal = {Compositio Mathematica},
keywords = {smooth, Hausdorff, second countable manifold; space of smooth complex valued functions; multidifferential operators; -graded Lie algebras; Hochschild cochains; Hochschild coboundary; nc elements; isomorphism on cohomology; homotopy maps; skew-symmetrization; star products; deformations; linear local maps},
language = {eng},
number = {1},
pages = {99-109},
publisher = {Kluwer Academic Publishers},
title = {An homotopy formula for the Hochschild cohomology},
url = {http://eudml.org/doc/90358},
volume = {96},
year = {1995},
}

TY - JOUR
AU - De Wilde, M.
AU - Lecomte, P. B. A.
TI - An homotopy formula for the Hochschild cohomology
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 96
IS - 1
SP - 99
EP - 109
LA - eng
KW - smooth, Hausdorff, second countable manifold; space of smooth complex valued functions; multidifferential operators; -graded Lie algebras; Hochschild cochains; Hochschild coboundary; nc elements; isomorphism on cohomology; homotopy maps; skew-symmetrization; star products; deformations; linear local maps
UR - http://eudml.org/doc/90358
ER -

References

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  2. 2 M. Cahen, M. De Wilde, S. Gutt: Local cohomology of the algebra of C∞ functions on a connected manifold. Lett. Math. Phys.4 (1980), pp.157-167. Zbl0453.58026
  3. 3 M. De Wilde, P. Lecomte: Formal deformations of the Poisson Lie algebra of a symplectic manifold and star-products. Existence, equivalence, derivations in: Deformations Theory of Algebras and Structures and Applications, M. Hazewinkel and M. Gerstenhaber, Eds., NATO ASI Series C, Vol. 247 (1988), pp. 897-960. Zbl0685.58039MR981635
  4. 4 M Gerstenhaber:The cohomology structure of an associative ring. Annals of Math.78 (1963), pp. 264-288. Zbl0131.27302MR161898
  5. 5 M. Gerstenhaber, S.D. Schack: Algebraic Cohomology and deformation theory in: Deformations Theory of Algebras and Structures and Applications, M. Hazewinkel and M. Gerstenhaber, Eds., NATO ASI Series C, Vol. 247 (1988), pp. 11-264. Zbl0676.16022MR981619
  6. 6 S. Gutt: An explicit *-product on the cotangent bundle of a Lie group. Lett. Math. Phys.7 (1983), pp. 249-258. Zbl0522.58019MR706215
  7. 7 G. Hochschild, B. Kostant, A. Rosenberg: Differential forms on regular affine algebras. Trans. Amer. Math. Soc.102 (1962), pp. 383-408. Zbl0102.27701MR142598
  8. 8 S. Maclane: Homology. Grundlehren der Math. Wissenschaften, 114, Springer-Verlag, Berlin (1963). Zbl0133.26502MR156879
  9. 9 J. Peetre: Une caractérisation abstraite des opérateurs différentiels. Math. Scandinavica7 (1959), pp. 211-218 and ibid. 8 (1960), pp. 116-120. Zbl0097.10402MR112146
  10. 10 J. Vey: Déformations du crochet de Poisson d'une variété symplectique. Comm. Math. Helv.50 (1975), pp. 421-454. Zbl0351.53029MR420753

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