Max-Albert Knus

Max-Albert Knus is a Swiss mathematician specializing in algebra.

He was born April 14, 1942, in Peseux, Neuchatel.

He was a Batelle-fellow at ETH and Brandeis University. He was director of research at University of Geneva. In 1969 he returned to ETH as a professor and became emeritus in 2007.

Knus expanded algebraic number theory to include a wider variety of structures. The classical study considers algebras over a field, whereas Knus considers algebras over a ring as in his monograph Quadratic and Hermitian Forms over Rings (1991). I am deeply grateful to them for doing mathematics in Bombay, Lausanne or Zurich."

Then in 1998 Knus joined Alexander Merkurjev, Markus Rost, and Jean-Pierre Tignol to write The Book of Involutions This book is about "central simple algebras with involution, in relation to linear algebraic groups."

His research interests include Galois cohomology.

Since 1997 he has been a fellow of the Swiss National Science Foundation.

Selected works 1974: (with Manuel Ojanguren) Théorie de la Descente et Algèbres d'Azumaya, Lecture Notes in Mathematics #389, Springer-Verlag 1974: "A Mayer-Vietoris sequence for the Brauer group", Journal of Pure and Applied Algebra 5: 345 to 60 1978: (with M. Ojanguren & R. Sridharan) "Quadratic forms an Azumaya algebras", Journal für die reine und angewandte Mathematik 303/4: 231 to 48 1980: (with R. Parimala) "Quadratic forms associated with projective modules over quaternion algebras", Crelle's Journal 318: 20 to 31 1985: (with A. Paques) "Quadratic spaces with trivial Arf invariant", Journal of Algebra 93: 267 to 91 1986: (with R. Parimala & R. Sridharan) "On rank 4 quadratic spaces with given Arf and Witt invariants", Mathematische Annalen 274: 181 to 95 1988: "Pfaffians and quadratic forms", Advances in Mathematics 71(1): 1 to 20 1988: Quadratic forms, Clifford algebras and spinors, Seminarios de Mathematicas, IMEEC, Unicamp, Campinas SP, Brazil 1989: (with R. Parimala and R. Sridharan) "A classification of rank 6 quadratic spaces via pfaffians", Journal für die reine und angewandte Mathematik 398: 187 to 218. 1990: (with R. Parimala and V. Srinivas) "Azumaya algebras with involutions", Journal of Algebra 130(1): 65 to 82 1991; (with R. Parimala & R. Sridharan) "Pfaffians, central simple algebras and similitudes", Mathematische Zeitschrift 206: 589 to 606 1991: Quadratic and Hermetian Forms over Rings, Grundlehren der Mathematischen Wissenschaften, Springer 1991: "Involutions on rank 10 central simple algebras", Journal of the Indian Mathematical Society (N.S.) 57(1-4): 143 to 151 1991: "On the discriminant of an involution", Bulletin of the Belgian Mathematical Society - Simon Stevin Ser A 43(1-2): 89 to 98 1991: "The Clifford algebra of a metabolic space", Archivum Mathematicum 56: 440 to 5 1991: "Pfaffians, central simple algebras and similitudes", Mathematische Zeitschrift 206(4): 589 to 604 1993: "Sur la form d'Albert et le produit tensoriel de deux algebras de quaternions", Bulletin of the Belgian Mathematical Society - Simon Stevin Ser B 45(3) : 333 to 7 1994: "On compositions and triality", Journal für die reine und angewandte Mathematik 457: 45 to 70 1995: (with T.Y. Lam, D.B. Shapiro, and J-P. Tignol) "Discriminants of involutions on biquaternion algebras", pages 279 to 303 in K-theory and algebraic geometry: connections with quadratic forms and division algebras, B. Jacob and A. Rosenberg, editors, American Mathematical Society 1998: "Cohomologie étale et groupe de Brauer", pages 210 to 28 in Group de Brauer, Lecture Notes in Mathematics # 844 1998: (with Alexander Merkurjev, Markus Rost, Jean-Pierre Tignol) The Book of Involutions, American Mathematical Society