M.-A. Knus, List of Publications M.-A. Knus, List of Publications


  1. (with M. Ojanguren) Théorie de la descente et algèbres d'Azumaya, Springer LN in Mathematics 389 (1974), 163 p.
  2. Quadratic forms, Clifford algebras and Spinors, Lecture notes, 136 pages, Seminars in Mathematics 1, Campinas, 1988. pdf (924KB)

  3. Quadratic and Hermitian Forms over Rings, Grundlehren der mathematischen Wissenschaften, Bd. 294, Springer-Verlag, 1991.

  4. (with A. A. Merkurjev, M. Rost and J.-P. Tignol) The Book of Involutions, Colloquium Publications Vol. 44, Amer. Math. Society, 1998, XXI + 593 pages.

Scientific Papers

Underlined articles may be downloaded as pdf or ps files. Unless mentioned otherwise, this is the latest preprint version of the article, which may differ slightly from the published version.

  1. Sur une classe d'algèbres filtrées. Comm. Helv. Math. 42 (1967), 111-132.

  2. (with U. Stammbach) Anwendungen der Homologietheorie der Liealgebren auf Zentralreihen und auf Präsentierungen, Comm. Hel. Math. 42 (1967), 197-306.

  3. Homology and homomorphisms of rings, J. of Algebra 9 (1968), 273-284.

  4. A Generalization of Clifford algebras, Math. Z. 110 (1969), 171-176.

  5. On the enveloping algebra and the descending central series of a Lie algebra, J. of Algebra 12 (1969), 335-338.

  6. Un théorème de cancellation pour les algèbres d'Azumaya, in ``Sur quelques problèmes d'algèbre'', Publ. no. 52 U.E.R. de Mathématiques Montpellier, 4 (1968/69), 9-24.

  7. Algebras graded by a group, Springer LN 92 (1969), 117-133.

  8. Sur le théorème de Skolem-Noether et sur les dérivations des algèbres d'Azumaya, C.R. Acad. Sciences. Paris t. 270 (1970), 637-639.

  9. Algèbres d'Azumaya et modules projectifs, Comm. Helv. Math. 45 (1970), 372-383.

  10. Sur le théorème de Skolem-Noether, in C.R. du 2ème K-Colloque, Publ. No 100, U.E.R. de Mathématiques Montpellier (1970/71), 60-66.

  11. (with M. Barr) Extensions of derivations, Proc. Am. Math. Soc. 28 (1971), 313-314.

  12. (with M. Ojanguren) Sur le polynôme caractéristique et les automorphismes des algèbres d'Azumaya, Ann. Scuola Normale Sup. Pisa 26 (1972), 225-231.

  13. (with M. Ojanguren) A note on the automorphisms of of maximal orders, J. of Algebra 22 (1972), 573-577.

  14. (with M. Ojanguren) Sur quelques applications de la théorie de la descente à l'étude du groupe de Brauer, Comm. Math. Helv. 47 (1972), 532-542.

  15. (with M. Ojanguren) A Mayer-Vietoris sequence for the Brauer group Journal of pure and appl. Algebra 5 (1974), 345-360.

  16. (with M. Ojanguren) A norm for modules and algebras, Math. Z. 142 (1975), 33-45.

  17. (with M. Ojanguren und D. Saltman) On Brauer groups in characteristic p, Springer LN in Mathematics 549 (1976), 25-49.

  18. (with F.R. De Meyer) The Brauer group of affine curve, Proc. Am. Math. Soc. 57 (1976), 227-232.

  19. (with M. Ojanguren) Modules and quadratic forms over polynomial algebras, Proc. Am. Soc. 66 (1977), 223-226.

  20. Formes quadratiques et algèbres d'Azumaya, C.R. du Colloque sur les formes quadratiques, Montpellier 1977, Bull. Soc. Math. de France, Mémoire 59 (1979), 95-100.

  21. Modules quadratiques sur un anneau de polynômes, Topology and Algebra, Proceedings of a Colloquium in Honor of B. Eckmann, 280 S., Monographie No 26, L'Enseignement Mathématique, 1978, 179-185.

  22. (with M. Ojanguren and R. Sridharan) Quadratic forms and Azumaya algebras. J. reine und angew. Mathematik 303/304 (1978), 231-248.

  23. (with R. Parimala) Quadratic forms and projective modules, 24 p., 1978, Preprint, Forschunsinstitut für Mathematik ETH.

  24. (with R. Parimala) Quadratic forms associated with projective modules over quaternion algebras, J. Reine Angew. Math.318 (1980), 20-31. (=27)

  25. (with M. Ojanguren) Cohomologie étale et groupe de Brauer, Springer LN 844 (Groupe de Brauer, Les Plans-sur-Bex, 1980), 210-228.

  26. (with R. Parimala and R. Sridharan) Non-free projective modules over H[x,y] and stable bundles over P2(C), Inventiones Math. 65 (1981), 13-27.

  27. Quaternionic modules over P2(R), Proceedings of the Antwerp Conference on Brauer groups, Springer L.N. 917, 1982, 245-259.

  28. Quaternionen über Polynomringe, quadratische Formen über R[x,y] und Vektorbündel über P2(C), Festband der Dedekind-Tagung 1981, Abh. der Braunschw. Wiss. Gesellschaft Bd.33 (1982), 165-168.

  29. (with M. Ojanguren and R. Parimala) Positive definite quadratic bundles over the projective plane, Comment. Math. Helvetici 57 (1982), 400-411.

  30. (with A. Paques) Quadratic spaces with trivial Arf invariant, J. of Algebra 93 (1985), 267-291.

  31. Bundles on P2 with a quaternion structure, Proceedings, International Colloquium on vector bundles, Bombay 1984, Oxford University Press, (1987), 225-250.

  32. with R. Parimala and R. Sridharan) On rank 4 quadratic spaces with given Arf and Witt invariants, Math. Ann. 274 (1986), 181-198.

  33. (with M. Kneser, M. Ojanguren, R. Parimala and R. Sridharan) Composition of quaternary quadratic forms, Compositio Mathematica 69 (1986), 133-150.

  34. Quadratic spaces and central separable algebras over polynomial rings, Seminars in Mathematics 3, Campinas 1988, 86-99.

  35. Pfaffians and quadratic forms, Adv. of Math. 71 (1988), 1-20.

  36. (with R. Parimala and R. Sridharan) A classification of rank 6 quadratic spaces via pfaffians, J. reine und angewandte Mathematik 398 (1989), 187-218.

  37. (with R. Parimala and V. Srinivas) Azumaya algebras with involutions, J. of Algebra 130 (1990), 65-82.

  38. (with R. Parimala and R. Sridharan) Pfaffians, central algebras and similitudes, Math. Z. 206 (1991), 589-604.

  39. (with M. Ojanguren) The Clifford algebra of a metabolic space, Archiv Math. 56 (1991), 440-445.

  40. (with A. Schofield) Aspects of the pfaffian, Comm. Algebra 19 (1991), 1959-1969.

  41. (with R. Parimala and R. Sridharan) Involutions on rank 16 central simple algebras, J. Indian Math. Soc. 57 (1991), 143-151. pdf (9300KB)

  42. (with R. Parimala and R. Sridharan) On the discriminant of an involution, Bull. Soc. Math. Belg. 43 (1991), 90-98. pdf (92KB)

  43. Sur la forme d'Albert et le produit tensoriel de deux algèbres de quaternions, Bull. Soc. Math. Belg. 45 (1993), 333-337. pdf (90KB) postscript (89KB)

  44. (with W. Bichsel) Quadratic forms with values in line bundles, Contemporary Mathematics 155 (1994), 293-306. pdf (237KB) postscript (239KB)

  45. (with R. Parimala and R. Sridharan) On compositions and triality, J. reine angew. Math. 457 (1994), 45-70. pdf (210KB)

  46. (with T.Y. Lam, D.B. Shapiro and J.-P. Tignol) Discriminants of involutions on biquaternion algebras, Proceedings of Symposia in Pure Mathematics 58.2 (1995), 279-303.

  47. (with D.E. Haile) On division algebras of degree 3 with involution, J. Algebra, 184 (1996), 1073-1081. pdf (186KB) postscript (157KB)

  48. (with D.E. Haile, M. Rost and J.-P. Tignol) Algebras of odd degree with involution, trace forms and dihedral extensions, Israel J. Math. 96 (1996), 299-340. pdf (426KB) postscript (394KB)

  49. (with A. Paques) On cubic étale algebras, Abh. Math. Sem. Univ. Hamburg 67 (1997), 281-295. pdf (245KB) postscript (223KB)

  50. (with O. Villa) Quadratic quaternion forms, involutions and triality, Documenta Mathematica, Quadratic Forms LSU (2001), 201-218. pdf (298KB) postscript(389KB)

  51. (with R. Parimala, R. Sridharan) On generic triality, Proceedings of the International Colloquium on Algebra and Geometry, Mumbai 2000, Naroda Publishing House (2002), International Distribution by Amer. Math. Soc., 355-404. pdf (544KB) postscript (544KB)

  52. (with J.-P. Tignol) Quartic exercices, Int. J. Math. and Math. Sci. 68 (2003), 4263-4323. pdf (583KB) postscript (588KB)

  53. (with L. Cadorin, M. Rost) On the dimension and other numerical invariants of algebras and vector products, Proceedings of the International Conference on Algebra and Number Theory, Hyderabad 2003, Hindustan Book Agency, New Delhi, (2005), 34-65. pdf (412KB) postscript (2252KB)

  54. Trialitarian automorphisms of Lie algebras. Transform. Groups 14 (2009), no. 2, 361--386. pdf (244KB) postscript (552KB)

  55. (with J-P. Tignol) Triality and étale algebras, Quadratic forms, linear algebraic groups, and cohomology. Dev. Math., 18 (2010) 259-286, Springer, New York. pdf (296KB) postscript (2464B)

  56. (with J-P. Tignol) Thin Severi-Brauer varieties, Pure and Applied Mathematics Quarterly 7, No 3 (2011). (Special Issue: In honor of Jacques Tits), 745-782. pdf (313KB) postscript (2240KB)
  57. (with V. Chernousov and J-P. Tignol) Conjugacy classes of trialitarian automorphisms and symmetric compositions, J. Ramanujan Math. Soc. 27, No.4 (2012), 479-508. pdf (258KB)
  58. (with V. Chernousov, A. Elduque and J-P. Tignol) Algebraic Groups of Type D_4, Triality, and Composition Algebras, Documenta Math. 18 (2013), 413--468. pdf (521KB)
  59. (with J-P. Tignol) Quadratic forms, compositions and triality over F_1, Expo. Math. 31 (2013), 305--333. pdf (384KB)
  60. (with J-P. Tignol) Triality and algebraic groups of type ^3D_4, Documenta Math. Extra Volume: Alexander S. Merkurjev's Sixtieth Birthday (2015) 387--405. pdf (222KB)

Unpublished Papers, Lecture notes

  1. A Teichmüller cocycle for finite extensions, Preprint, 1975, 21 p. pdf (964KB)

  2. On cubic algebras, Notes for a Mini-course, Campinas, September 1996, 49 p. pdf (246KB)

  3. Notes on triality, Notes for a Mini-course, Lens, June 1999, 28 p. pdf (246KB)

  4. (with H. J. Hoehnke) Algebras, their Invariants and K-forms. A tribute to [the work of] HEINRICH BRANDT on the 50th anniversary of his death, 25 p., 2004. pdf (393KB) postscript (372KB)

General Papers

  1. Quelques problèmes d'existence en algèbre, plaquette du centenaire, Gymnase cantonal, Neuchâtel 1973. 183-192.

  2. Christoffel und die Mathematik an der polytechnischen Schule Zürich, in : E.B. Christoffel, The Influence of his Work on mathematics and the Physical Sciences, p. 33-41, Birkhäuser, 1981.

  3. 150. Geburtstag von Richard Dedekind (1831-1916), ETH Bulletin 166, Oktober 1981, ETH Zürich.. pdf (139KB)

  4. Dedekind und das Polytechnikum in Zürich, Festband der Dedekind-Tagung 1981, Abh. der Braunschw. Wiss. Gesellschaft Bd.33 (1982), 43-60.

  5. A brief panorama of mathematics in Switzerland, The Zürich Intelligencer, Springer-Verlag, August 1994. pdf (253KB)

  6. Von Familien, Wunderkindern und Autodidakten, unizürich 2/94, 6-8, appeared also in Bulletin, Magazin der ETH 254, Juni 1994, 4-7 and Vermessung, Photogrammetrie, Kulturtechnik 8/94, 373-374. pdf (450KB)

  7. Au Poly? An der ETH?, Kleine Schriften, ETH Zürich, Januar 1997, 9 Seiten. pdf (4004KB)

  8. (with G. Mislin und U. Stammbach) Beno Eckmann 1917--2008. Jahresber. Dtsch. Math.-Ver. 112, No. 1, 25-50 (2010).
    pdf (507kb)

  9. Book review of math.ch/100 Schweizerische mathematische Gesellschaft société mathématique suisse Swiss Mathematical Society 1910--2010. Math. Intelligencer 34 (2012), no. 1, 65--68. pdf

  10. Historisches Lexikon der Schweiz. Biographical notices for

    Carl Adams (1811-1849)
    Heinrich Burkhardt (1861-1914)
    Elwin Bruno Christoffel (1829-1900)
    Richard Dedekind (1831-1916)
    André Haefliger (1929-)
    Adolf Hurwitz (1859-1919)
    Jürgen Moser (1928-1999)
    Georges de Rham (1903-1990)


  1. (with G. Mislin und U. Stammbach) Herausgabe von: Topology and Algebra, Proceedings of a Colloquium in Honor of B. Eckmann, 280 S., Monographie No 26, L'Enseignement Mathématique, 1978.

  2. (with W. Scharlau), Richard Dedekind, Vorlesung über Differential-und Integralrechnung 1861/62, Dokumente zur Geschichte der Mathematik Bd.1, Vieweg, 1985.

  3. (with G. Mislin and U. Stammbach) Selecta Beno Eckmann. Springer-Verlag, 1987.