Richard KERNER
PUBLICATIONS
Concerning the Non-Commutative Geometry
Before 1989
1. Generalization of the Kaluza-Klein theory, Ann. Inst. H. Poincaré, 9 (2), 141-150 (1968).
2. Sur une représentation fidèle de l'algèbre de Poisson, C.R. Acad. Sci. Paris, 269 (1969).
3. Sur les équations invariantes sur un espace fibré principal, C.R. Acad. Sci. Paris, 272 (1971).
4. Invariant equations on fibre bundles, dans le livre "Group theoretical methods in Physics", ed. Janner & Jensen, Springer-Verlag, p. 80-86 (1976) .
5. Gauge fields on the supersymmetric spaces, dans le livre "Group theoretical methods in physics", ed. Scharp & Kolman, Acad. Press, N.Y., p. 321-328, (1977).
6. Spinors on fibre bundles, dans le livre "Group Theoretical methods in physics", Tel-Aviv University Press, Math. Ser., 3, 254-256, (1980).
7. Spinors on fibre bundles and their use in invariant models, dans le livre "Differential Geometry and Physics", Springer-Verlag, Math. Ser., 349-358, (1980).
8. Covariant objects and invariant equations on fibre bundles, Journal of Mathematical Physics, 21 (10), 2553-2559, (1980).
9. Geometrical background for the Unified Theories, Ann. Inst. H. Poincaré, 34 (4), 437-463, (1981).
10. Graded fibre bundles and unified field theories, Physica A, 143, 389-392, (1982).
11. Multiple fibre bundles and higher order gauge theories, Journ. Math. Phys., 24 (2), 356-360, (1983).
12. Graded gauge theories over supersymmetric space, (en collaboration avec E.M. da Silva Maia) Journ. Math. Phys., 24 (2), 361-368, (1983).
13. Super-symmetric Kaluza-Klein Theory, Nuovo Cimento A, 73 (3), 309-326, (1983).
14. Graded Gauge Theory, Comm. Math. Phys., 91, 213-231, (1983).
15. Gauge symmetries in Multiple Fibre Bundles, CERN preprint TH 3669 (1983).
16. Théories de Jauge Graduées, dans le livre "Differential Geometry Mehtods in Mathematical Physics", ed. S. Sternberg, D. Reidel pub. Comp., pp. 23-43, (1984).
17. Two-level Kaluza-Klein theory, en collaboration avec L. Nikolova et V. Rizov, Lett. Math. Phys., 14, 333-341, (1987).
18. Geometry of Kaluza-Klein theories, dans Proceedings of the Poiana-Brasov Summer School, ed. Dita et Georgescu, Acad. Press, 243-284, (1989).
After 1989
19. Classical Bosons in the non-commutative geometry, (avec M. Dubois-Violette et J. Madore), Class. & Quant. Gravity, 6, 1709-1724, (1989).
20. Généralisation de la supergravité à 11 dimensions avec les invariants d'Euler, (avec J.C. Fabris), Helvetica Physica Acta, 62, 427, (1989).
21. Non-Commutative geometry and Classical Field Theory (avec M. Dubois-Violette et J. Madore), Phys. Lett. B, 217, 485, (1989).
22. Modèles des Théories de Jauge basés sur la géométrie non-commutative, (avec M. Dubois-Violette et J. Madore), dans les proceedings des Journées Relativistes 1989, Barrabes & Boisseau ed., Annales de Physique, 14 (Suppl. au n°6), 127-138, (1989).
23. Non-Commutative differential geometry of matrix algebras (avec M. Dubois-Violette et J. Madore), Journ. Math. Phys., 31 (2), 316-323, (1990).
24. Non-commutative geometry and new models of gauge theories, (avec M. Dubois-Violette et J. Madore), Journ. Math. Phys., 31 (2), 323-331, (1990).
25. Non-Singular exact cosmological solution of a 5-dimensional super-gravity, (avec R. Balbinot et J.C. Fabris), Class. & Quant. Gravity, 7, 17, (1990).
26. Gauge theories based on the non-commutative geometry, dans les proceedings du Workshop "Quantum Groups", ed. H.D. Doebner & J.D. Hennig, Springer-Verlag, Lecture Notes in Physics, 370, 398-425, (1990).
27. Recent progress in non-commutative geometry, Proceedings de XVIII ICGTMP Conference de Moscou, ed. V.V. Dodonov et V.I. Manko, Springer-Verlag, Lecture Notes in Physics, 382, 233-240, (1991).
28. Supermatrix geometry, (avec M. Dubois-Violette et J. Madore), Class. and Quant. Grav., 8, 1077-1089, (1991).
29. Graduation Z3 et la racine cubique de l'équation de Dirac, C.R. Acad. Sci. Paris, 312 (série II), 191-196, (1991).
30. Z3-graded algebras and the cubic root of the Dirac operator, Journ. of Math. Phys., 33 (1), 403-411, (1992).
31. Z3-grading and the cubic root of the Dirac equation, Class. and Quant. Grav., 9, 137-146, (1992).
32. Generalization of Manton's construction of the Weinberg-Salam model with Gauss-Bonnet term (avec Ch. Bertrand et S. Mignemi), Int. Journal of Modern Physics A, 7 (31), 7741-7752, (1992).
33. Graded non-commutative geometries, Journ. of Geometry and Physics, 11 (1-4), 325-335, (1993).
34. Z-grading and ternary algebraic structures, dans le livre en l'honneur de L.C. Biedenharn, "Symmetries in Science VI", ed. B. Gruber, Plenum Press, 373-388, (1993).
35. Z3-graded algebras and non-commutative gauge theories, dans le livre "Spinors, Twistors, Clifford Algebras and Quantum Deformations", Eds. Z. Oziewicz, B. Jancewicz, A. Borowiec, pp. 349-357, Kluwer Academic Publishers (1993) .
36. Z3-grading and ternary algebraic structures, dans les Proceedings du Workshop "New Symmetries and Differential Geometry", Clausthal 1993, V. Dobrev, M.D. Doebner and S. Ushveridze eds., pp. 375-394, World Scientific (1994).
37. Non-commutative geometry, dans "Mathematical Physics towards the 21st century", R.N. Sen & A. Gersten eds., Ben Gurion University of the Negev Press, pp. 112-129, (1994).
38. Ternary structures and the Z3-grading, dans "Quantum Groups : Formalism and Applications", Proceedings of the XXX Karpacz Winter School of Theoretical Physics, J. Lukierski, Z. Popowicz & J. Sobczyk eds, Polish Scientific Publ., pp. 605-617, (1995).
39. Calcul différentiel extérieur Z3-gradué, C.R. Acad. Sci. Paris, Série IIb, 320, 587-592, (1995).
40. Z3-graded ternary algebras, new gauge theories and quarks, dans Proceedings du Workshop "Topics in Quantum Field Theory", Maynooth 1995, T. Tchrakian, ed. World Scientific, pp. 113-126, (1995).
41. Classical motions in q-deformed phase space (en coll. avec J. Wess et A. Lorek), C. R. Acad. Sci. Paris, 322, Série IIb, 211-218, (1996).
42. Z3-graded exterior differential calculus and gauge theories of higher order, Lett. in Math. Phys., 36, 441-454, (1996).
43. Exterior differential calculus with Z3-grading, Actes du Colloque en l'honneur de A. Lichnerowicz, G. Ferrarese ed., Editions Pitagora, Bologna, pp. 75-89, (1996).
44. On special classes of n-algebras, (en coll. avec L. Vainerman), Journ. in Math. Phys., 37 (5), 2553-2565, (1996).
45. Universal q-differential calculus and q-analog of homological algebra (en coll. avec M. Dubois-Violette), Acta Math. Univ. Comenianae, LXV (2), 175-188, (1996).
46. Extensions of differential calculus with ZN-grading, Proceedings of the Conference on Geometry and Physics (Vietri, Italie, Septembre 1996), G. Marmo & A. Simoni eds, Rendiconti di Seminario Matematico Univ. Politecn. Torino, 54, 4, (1996).
47. A few thoughts about quarks, Turkish Journ. of Physics, édition spéciale à la mémoire de A. Barut, 21 (3), 415-424, (1997).
48. The cubic chessboard, Class. Quantum Grav., édition spéciale en l'honneur de A.Trautman, 14 (1A), A203-A225, (1997).
49. Hypersymmetry : a Z3-graded generalization of supersymmetry, (en coll. avec V.Abramov et B. Le Roy), Journ. in Math. Phys., 38 (3), 1650-1669 , (1997).
50. Universal ZN-graded differential calculus (en coll. avec M. Dubois-Violette), Journal. of Geometry and Physics, 23, 235-246, (1997).
51. ZN-graded differential calculus, Proc. of the 5th Intern. Colloquium on "Quantum Groups and Integrable Systems" (Prague, 20-22 June 1996), Czech. Journ. of Physics, 47 (1), 33-40, (1997).
52. ZN-graded algebras and N-th order q-differential calculus, Proc. of Group 21 ICGTMP, Goslar (Allemagne, Juillet 1996), H.D. Doebner, W. Scherer, C. Schulte eds, World Scientific, Vol. 2, 193-198, (1997).
53. Differential exterior calculus with ZN-grading, Proceedings of the Max Born Meeting (Karpacz, Pologne, Septembre 1996), Z. Borowiec & J. Lukierski eds, PWN (Varsovie), (1997).
54. Covariant q-differential calculus, Proceedings du Colloque de Physique Mathé-matique (Istanbul, Sept. 1997), Turkish Journ. of Physics, à paraître, (1998).
55. Shadow of noncommutativity, (en coll. avec M. Dubois-Violette et J. Madore), J. Math. Phys., 39 (2), 730-738, (1998).
56. A q-deformed differential calculus at roots of unity, Proceedings of the 7th Intern. Colloquium on Quantum Groups and Integrable Systems (Prague, Juin 98), Czech. Journ. of Phys., 48 (11), 1387-1394, (1998).
57. Covariant q-differential calculus and its deformations at qN = 1, (en coll. avec B. Niemeyer), Lett. in Math. Phys., 45,161-176, (1998).
58. On certain realizations of q-deformed exterior differential calculus, (en coll. avec V. Abramov), Reports on Math. Phys., 43 (1/2), 179-194, (1999).
60. Non commutative extensions of classical theories in physics, dans le livre " Towards Quantum Gravity ", Ed. J. Kowalski-Glikman, Springer Lecture Notes in Physics, LNP 541, pp. 130-157, (2000).
61. Exterior differentials of higher order and their covariant generalization (en collaboration avec V. Abramov), Journ. of Math. Physics 41 N°8, pp. 5598-5614, (2000)
62. Ternary algebraic structures in theoretical physics, dans les Actes du Congrès " ICGTMP –2000", Dubna (Russie), à paraître en 2001, math-ph/0011023
Another development concerns possible generalizations and extensions of usual NCG. One direction is represented by Z_3 and more generally, Z_N grading (represented mostly by papers No. 29, 30, 39, 42, 48, 49, 50, 57, 58, 61. 63 (the last one on the list).
Finally, one can include also the works on the q-deformed spaces and q-deformed differential calculi: items 41, 45, 56.