Max-Albert Knus is a Swiss mathematician specializing in algebra.
He was born April 14, 1942, in Peseux, Neuchatel. He studied mathematics at ETH Zurich with Beno Eckmann and K. Chandrasekharan, graduating in 1967 with a PhD thesis titled On a class of filtered algebras.
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, Max-Albert @ ZbMATH Open
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). In the preface he acknowledges colleagues that contributed to the science: "Many results in this book were developed by (or in collaboration with) Raman Parimala, Ramaiyengar Sridharan and Manuel Orjanguran.Manuel Orjanguran @ %C3%89cole_Polytechnique_F%C3%A9d%C3%A9rale_de_Lausanne 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 published by the American Mathematical Society. Knus, Merkerjev, Rost, & Tignol (1998) The Book of Involutions @ AMS 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.Max-Albert Knus @ 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 D.W. Lewis (March 1992) Review: Quadratic and Hermetian Forms over Rings, Bulletin of the Irish Mathematical Society 28: 68,9 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
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