Background
Serre, Jean-Pierre was born on September 15, 1926 in Bages, France. Son of Jean and Adèle (Diet) Serre.
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(The main general theorems on Lie Algebras are covered, ro...)
The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I. I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal,.. This part has been written with the help of F.Raggi and J.Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo- tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A (R)i A -+ A2A -+ A i.e., ifwe denote the imageof(x,y) under this map by [x,y) then the condition becomes for all x e k. [x,x)=0 2). (lx,II], z]+ny, z), x) + ([z,xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/,x).
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(This is an updated English translation of "Cohomologie Ga...)
This is an updated English translation of "Cohomologie Galoisienne", published more than 30 years ago as one of the very first Lecture Notes in Mathematics (LNM 5). It includes a reproduction of an influential paper of R. Steinberg, together with some new material and an expanded bibliography.
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(This volume addresses algebraic invariants that occur in ...)
This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry. It is hoped that these new invariants will prove similarly useful. Early versions of the invariants arose in the attempt to classify the quadratic forms over a given field. The authors are well-known experts in the field. Serre, in particular, is recognized as both a superb mathematician and a master author. His book on Galois cohomology from the 1960s was fundamental to the development of the theory. Merkurjev, also an expert mathematician and author, co-wrote The Book of Involutions (Volume 44 in the AMS Colloquium Publications series), an important work that contains preliminary descriptions of some of the main results on invariants described here. The book also includes letters between Serre and some of the principal developers of the theory. It will be of interest to graduate students and research mathematicians interested in number theory and Galois cohomology.
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(This is an English translation of the now classic "Algbre...)
This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.
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( This is an updated English translation of Cohomologie G...)
This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.
http://www.amazon.com/Galois-Cohomology-Springer-Monographs-Mathematics/dp/364263866X%3FSubscriptionId%3DAKIAJRRWTH346WSPOAFQ%26tag%3Dprabook0b-20%26linkCode%3Dsp1%26camp%3D2025%26creative%3D165953%26creativeASIN%3D364263866X?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook0b-20&linkCode=sp1&camp=2025&creative=165953&SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook0b-20&linkCode=sp1&camp=2025&creative=165953
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(NY 1965 Benjamin. 1964 Lectures given at Harvard Unversit...)
NY 1965 Benjamin. 1964 Lectures given at Harvard Unversity. 4to., about 200pp., wraps. VG, light cover wear.
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Serre, Jean-Pierre was born on September 15, 1926 in Bages, France. Son of Jean and Adèle (Diet) Serre.
Baccalauréat, Lycée de Nîmes, France, 1944. Agrégation, Ecole Normale Supérieure, France, 1948. Doctor of Philosophy, Sorbonne, 1951.
Doctor of Philosophy (honorary), Cambridge University, England, 1978. Doctor of Philosophy (honorary), University Stockholm, 1980. Doctor of Philosophy (honorary), University Glasgow, Scotland, 1983.
Doctor of Philosophy (honorary), University Athens, 1996. Doctor of Philosophy (honorary), Harvard University, 1998. Doctor of Philosophy (honorary), Durham University, 2000.
Doctor of Philosophy (honorary), London University, 2001. Doctor of Philosophy (honorary), University Oslo, 2002. Doctor of Philosophy (honorary), University Oxford, 2003.
Doctor of Philosophy (honorary), Academy Bucharest, 2004. Doctor of Philosophy (honorary), University Barcelona, 2004. Doctor of Philosophy (honorary), University Madrid, 2006.
Doctor of Philosophy (honorary), McGill University, 2008.
With Centre National de la Recherche Scientifique, Paris, 1948—1954, University Nancy, 1954—1956. Professor College de France, Paris, 1956—1994, professor emeritus.
(This volume addresses algebraic invariants that occur in ...)
( This is an updated English translation of Cohomologie G...)
(This is an updated English translation of "Cohomologie Ga...)
(This is an English translation of the now classic "Algbre...)
(The main general theorems on Lie Algebras are covered, ro...)
(NY 1965 Benjamin. 1964 Lectures given at Harvard Unversit...)
Author: Groupes algébriques et corps de classes, 1959, Corps Locaux, 1962, Lie Algebras and Lie Groups, 1965, Représentations linéaires des groupes finis, 1968, Cours d'arithmétique, 1970, Trees, 1980, Galois Cohomology, 1997, Local Algebra, 2000, Collected Papers, 1986, 2000.
Member Academy of Sciences Paris, Royal Society London (honorary fellow), London Mathematics Society (honorary), National Academy of Sciences United States (foreign), Nederland Academy of Sciences (foreign), Academy of Sciences Stockholm (foreign), Russian Academy of Sciences (foreign), Norwegian Academy of Sciences (foreign), Academy Simica Taiwan (foreign).
Married Josiane Heulot, August 10, 1948. 1 child, Claudine.