CoChat
Sign Up
Cited by 145Advanced Topics in AlgebraHomotopy and Cohomology in Algebraic TopologyAdvanced Algebra and Geometry

The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.

A Primer of Hopf Algebras

Cartier, Pierre·2007·Frontiers in Number Theory, Physics, and Geometry II
DOI 10.1007/978-3-540-30308-4_12
Open this paper in CoChat — free account

Overview

Integrity signals

Registry

Crossref · 10.1007/978-3-540-30308-4_12

Cites

6 of 6 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Citations

Cites

Show all 6 references

Research works printed but not linked: 66

  1. A. Borel, Sur l'homologie et la cohomologie des groupes de Lie compacts connexes, Amer. J. Math. 76 (1954), 273–342. Reprinted in Œuvres, Collected Papers, vol. 1, pp. 322–391, Springer, Berlin (1983). · DOI
  2. A. Borel, Topology of Lie groups and characteristic classes, Bull. Am. Math. Soc. 61 (1955), 397–432. Reprinted in Œuvres, Collected Papers, vol. 1, pp. 402–437, Springer, Berlin (1983). · DOI
  3. A. Borel, Sur la torsion des groupes de Lie, J. Math. Pures Appl. 35 (1955), 127–139. Reprinted in Œuvres, Collected Papers, vol. 1, pp. 477–489, Springer, Berlin (1983).
  4. A. Borel, Linear algebraic groups, 2nd edition, Springer, Berlin (1982).
  5. A. Borel (and C. Chevalley), The Betti numbers of the exceptional groups, Mem. Amer. Math. Soc. 14 (1955), 1–9. Reprinted in Œuvres, Collected Papers, vol. 1, pp. 451–459, Springer, Berlin (1983).
  6. N. Bourbaki, Groupes et algèbres de Lie, Chap. 1, and Chap. 2, 3, Hermann, Paris (1971 and 1972).
  7. N. Bourbaki, Groupes et algèbres de Lie, Chap. 4, 5 et 6, Masson, Paris (1981).
  8. N. Bourbaki, Algèbre, Chap. 1, 2 et 3, Hermann, Paris (1970).
  9. N. Bourbaki, Espaces vectoriels topologiques, Chap. 1 à 5, Masson, Paris (1981).
  10. R. Brauer, Sur les invariants intégraux des variétés des groupes de Lie simples clos, C.R. Acad. Sci. Paris 201 (1935), 419–421.
  11. E. Cartan, La géométrie des groupes simples, Annali di Mat. 4 (1927), 209–256. Reprinted in Œuvres Complètes, Part I, vol. 2, pp. 793–840, Gauthier-Villars, Paris (1952). · DOI
  12. E. Cartan, Sur les invariants intégraux de certains espaces homogènes clos et les propriétés topologiques de ces espaces, Ann. Soc. Pol. Math. 8 (1929), 181–225. Reprinted in Œuvres Complètes, Part I, vol. 2, pp. 1081–1126, Gauthier-Villars, Paris (1952).
  13. E. Cartan, La théorie des groupes finis et continus et l'Analysis Situs, Mém. Sci. Math., Vol. 42, Gauthier-Villars, Paris (1930). Reprinted in Œuvres Complètes, Part I, vol. 2, pp. 1165–1226, Gauthier-Villars, Paris (1952).
  14. P. Cartier, Dualité de Tannaka des groupes et algèbres de Lie, C.R. Acad. Sci. Paris 242 (1956), 322–325.
  15. P. Cartier, Théorie di.érentielle des groupes algébriques, C.R. Acad. Sci. Paris 244 (1957), 540–542.
  16. P. Cartier, Hyperalgèbres et groupes de Lie formels, Institut Henri Poincaré, Paris (1957).
  17. P. Cartier, Isogénies des variétés de groupes, Bull. Soc. Math. France 87 (1959), 191–220. · DOI
  18. P. Cartier, Groupes algébriques et groupes formels, in “Colloque sur la théorie des groupes algébriques” (Bruxelles, 1962), pp. 87–111, Gauthier-Villars, Paris (1962).
  19. P. Cartier, On the structure of free Baxter algebras, Adv. Math. 9 (1972), 253–265. · DOI
  20. P. Cartier, La théorie classique et moderne des fonctions symétriques, Astérisque 105–106 (1983), 1–23.
  21. P. Cartier, Jacobiennes généralisées, monodromie unipotente et intégrales itérées, Astérisque 161–162 (1988), 31–52.
  22. P. Cartier, Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents, Astérisque 282 (2002), 137–173.
  23. C. Chevalley, Theory of Lie groups, Princeton Univ. Press, Princeton (1946).
  24. C. Chevalley, Théorie des groupes de Lie, tome II: Groupes algébriques, Hermann, Paris (1951).
  25. A. Connes and M. Marcolli, Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory, in this volume, pages 617- 714. · DOI
  26. A. Connes and H. Moscovici, Hopf algebras, cyclic cohomology and the transverse index theorem, Comm. Math. Phys. 198 (1998), 199–246. · DOI
  27. A. Connes and H. Moscovici, Modular Hecke algebras and their Hopf symmetry, Moscow Math. J. 4 (2004), 67–109. · DOI
  28. P. Deligne, Le groupe fondamental de la droite projective moins trios points, in “Galois groups over Q” (edited by Y. Ihara, K. Ribet and J.-P. Serre), pp. 79–297, Springer, Berlin (1989). · DOI
  29. P. Deligne, Catégories tannakiennes, in “The Grothendieck Festschrift” (edited by P. Cartier and al.), vol. II, pp. 111–195, Birkhäuser, Boston (1990).
  30. M. Demazure and A. Grothendieck, Schémas en groupes, 3 vol., Springer, Berlin (1970). · DOI
  31. M. Demazure and P. Gabriel, Introduction to algebraic geometry and algebraic groups, North Holland, Amsterdam (1980).
  32. G. de Rham, Sur l'Analysis Situs des variétés à n dimensions, J. Math. Pures Appl. 10 (1931), 115–200.
  33. J. Dieudonné, Introduction to the theory of formal groups, Marcel Dekker, New York (1973).
  34. S. Doplicher and J.E. Roberts, Endomorphisms of C-algebras, cross products and duality for compact groups, Ann. of Math. 130 (1989), 75–119. · DOI
  35. S. Doplicher and J.E. Roberts, A new duality theory for compact groups, Invent. Math. 98 (1989), 157–218. · DOI
  36. Ch. Ehresmann, Sur la topologie de certains espaces homogènes, Ann. of Math. 35 (1934), 396–443. Reprinted in Charles Ehresmann: œuvres complètes et commentées, Vol. I, pp. 6–53, Amiens (1984). · DOI
  37. Ch. Ehresmann, Sur la topologie de certaines variétés algébriques réelles, J. Math. Pures Appl. 16 (1937), 69–100. Reprinted in Charles Ehresmann: œuvres complètes et commentées, Vol. I, pp. 55–86, Amiens (1984).
  38. Ch. Ehresmann, Sur la variété des génératrices planes d'une quadrique réelle et sur la topologie du groupe orthogonal à n variables, C.R. Acad. Sci. Paris 208 (1939), 321–323. Reprinted in Charles Ehresmann: œuvres complètes et commentées, Vol. I, pp. 304–306, Amiens (1984).
  39. Ch. Ehresmann, Sur la topologie des groupes simples clos, C.R. Acad. Sci. Paris 208 (1939), 1263–1265. Reprinted in Charles Ehresmann: œuvres complètes et commentées, Vol. I, pp. 307–309, Amiens (1984).
  40. I.M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V.S. Retakh and J.-Y. Thibon, Noncommutative symmetric functions, Adv. Math. 112 (1995), 218–348. · DOI
  41. F. Goichot, Un théorème de Milnor-Moore pour les algèbres de Leibniz, in “Dialgebras and related operads”, pp. 111–133, Springer, Berlin (2001). · DOI
  42. P.P. Grivel, Une histoire du théorème de Poincaré-Birkho.-Witt, Expo. Math. 22 (2004), 145–184. · DOI
  43. Harish-Chandra, Lie algebras and the Tannaka duality theorem, Ann. of Math. 51 (1950), 299–330. Reprinted in Collected Papers, vol. I, pp. 259–290, Springer, Berlin (1984). · DOI
  44. W.V.D. Hodge, The theory and applications of harmonic integrals (2nd edition), Cambridge University Press, Cambridge (1952).
  45. M. Hoffman, Quasi-shuffe products, J. Alg. Combinat. 11 (2000), 46–68.
  46. H. Hopf, Über die Topologie der Gruppen-Mannigfaltigkeiten und ihrer Verallgemeinerungen, Ann. of Math. 42 (1941), 22–52. Reprinted in Selecta Heinz Hopf, pp. 119–151, Springer, Berlin (1964). · DOI · Paper page
  47. D. Krob, B. Leclerc and J.-Y. Thibon, Noncommutative symmetric functions, II: transformations of alphabets, J. Algebra Comput. 7 (1997), 181–264. · DOI
  48. J. Leray, Sur l'homologie des groupes de Lie, des espaces homogènes et des espaces fibrés principaux, in “Colloque de Topologie Algébrique”, Bruxelles (1950), pp. 101–115. Reprinted in Œuvres scientifiques, vol. I, pp. 447–461, Springer, Berlin (1998).
  49. J. Leray, L'anneau spectral et l'anneau filtré 'homologie d'un espace localement compact et d'une application continue, J. Math. Pures Appl. 29 (1950), 1–139. Reprinted in Œuvres scientifiques, vol. I, pp. 261–401, Springer, Berlin (1998).
  50. J.-L. Loday and M. Ronco, Hopf algebra of the planar binary trees, Adv. Math. 139 (1998), 293–309. · DOI
  51. L. Loomis, An introduction to abstract harmonic analysis, van Nostrand Co, Princeton (1953).
  52. M. Lothaire, Algebraic combinatorics on words, Cambridge Univ. Press, Cambridge (2002). · DOI
  53. I.G. MacDonald, Symmetric functions and Hall polynomials (2nd edition), Oxford Univ. Press, New York (1995). · DOI
  54. C. Malvenuto and C. Reutenauer, Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra 177 (1995), 967–982. · DOI
  55. F. Patras, L'algèbre des descentes d'une bigèbre graduée, J. Algebra 170 (1994), 547–566. · DOI
  56. H. Poincaré, Analysis Situs, Journ. Ecole Polyt. 1 (1895), 1–121. Reprinted in Œuvres, vol. VI, pp. 193–288, Gauthier-Villars, Paris (1953).
  57. H. Poincaré, Sur les groupes continus, Camb. Phil. Trans. 18 (1899), 220–255. Reprinted in Œuvres, vol. III, pp. 173–212, Gauthier-Villars, Paris (1965).
  58. L.S. Pontrjagin, Homologies in compact Lie groups (in Russian), Math. Sbornik 6 (1939), 389–422.
  59. D. Quillen, Rational homotopy theory, Ann. of Math. 90 (1969), 205–295. · DOI
  60. C. Reutenauer, Free Lie algebras, Oxford Univ. Press, New York (1993). · DOI
  61. M. Ronco, A Milnor-Moore theorem for dendriform Hopf algebras, C.R. Acad. Sci. Paris (série I) 332 (2000), 109–114. · DOI
  62. M. Ronco, Eulerian idempotents and Milnor-Moore theorem for certain non-commutative Hopf algebras, J. Algebra 254 (2002), 152–172. · DOI
  63. N. Saavedra, Catégories tannakiennes, Springer, Berlin (1972).
  64. H. Samelson, Beiträge zur Topologie der Gruppen-Mannigfaltigkeiten, Ann. of Math. 42 (1941), 1091–1137. · DOI
  65. J.-P. Serre, Gèbres, Enseignement Math. 39 (1993), 33–85. Reprinted in Œuvres, Collected Papers, vol. IV, pp. 272–324, Springer, Berlin (2000).
  66. H. Weyl, The classical groups (2nd edition), Princeton University Press, Princeton (1946).

Cited by

Sorted by citations

Metadata

Authors
Cartier, P.
Affiliations
Centre National de la Recherche Scientifique (FR)
Corresponding author
Cartier, Pierre
Venue
Frontiers in Number Theory, Physics, and Geometry II
Publisher
Springer Berlin Heidelberg
Published
2007-07-17
Pages
537-615
DOI
10.1007/978-3-540-30308-4_12
OpenAlex
W1567985745
Cited by
145
References
6
Citations by year
2025: 5 · 2024: 2 · 2022: 8 · 2021: 10 · 2020: 34 · 2019: 8 · 2018: 16 · 2017: 7 · 2016: 10 · 2015: 11 · 2014: 3 · 2013: 7 · 2012: 4
FWCI
21.00
Type
book chapter
Language
en
Open access
closed
Locations
Springer eBooks (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Algebra and Number Theory › Advanced Topics in Algebra
  • Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
  • Physical Sciences › Mathematics › Algebra and Number Theory › Advanced Algebra and Geometry
Keywords
Hopf algebras, Lie groups, compact symmetric spaces, structure theorem, unipotent algebraic groups, polylogarithm functions, multiple zeta values

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review