5 Invariant Koszul Form of Homogeneous Bounded Domains …
91
Fig. 5.1 Henri Cartan lecture on homogeneous bounded domains, in Freiburg, March 13, 1987
value of your father’s ideas on the subject”. This citation makes reference to Elie
Cartan’s seminal work on symmetric bounded domains, exploited by carl-Ludwig
Siegel (Fig. 5.1).
During 50’s, Jean-Louis Koszul gave 3 Lectures in Sao Paulo entitled «Faisceaux
et Cohomologie»; «Variétés Kählériennes» and «Exposés sur les espaces homogènes
symétriques». Koszul visits to Brazil have been co-organized with a first visit to USP
in 1956 to give a course in August and September (lecture notes taken by José
de Barros Neto) on “Faisceaux et cohomologie” (general treatise on Cech cohomology with coefficients on a sheaf), published in 1957. A 2nd Course was given
in September and October of 1956 (lecture notes taken by Chaim Samuel Honig
and Carlos Benjamin de Lyra) on “Variétés Kâhlériennes”, published in 1957, and
also course on Multilinear Algebra, with notes by L. H. Jacy Monteiro, published in
1956. Last course on “Exposés sur les espaces homogènes symétriques ” was given
in September and October of 1958 with lecture notes published in 1959. R. Bott
commented on these seminars “very pleasant. The pace is fast, and the considerable material is covered elegantly. In addition to the more or less standard theorems
on symmetric spaces, the author discusses the geometry of geodesics, Bergmann’s
metrics, and finally studies the bounded domains with many details”.
Elected to Academia de Ciencias do Estado de Sao Paulo in 1981, Jean-Louis
Koszul visited USP again in 1986 for an inaugural talk at Instituto de Estudos
Avançados, hosted by A.A. M. Rodrigues on “The genesis of Bourbaki” (Fig. 5.2).
In the book “Selected papers of JL Koszul” [57], Koszul summarizes the work,
I will detail in the following: “It is with the problem of the determination of the
homogeneous bounded domains posed by E. Cartan around 1935 that are related
[my papers]. The idea of approaching the question through invariant Hermitian
forms already appears explicitly in Cartan. This leads to an algebraic approach
which constitutes the essence of Cartan’s work and which, with the Lie J-algebras,
91
Fig. 5.1 Henri Cartan lecture on homogeneous bounded domains, in Freiburg, March 13, 1987
value of your father’s ideas on the subject”. This citation makes reference to Elie
Cartan’s seminal work on symmetric bounded domains, exploited by carl-Ludwig
Siegel (Fig. 5.1).
During 50’s, Jean-Louis Koszul gave 3 Lectures in Sao Paulo entitled «Faisceaux
et Cohomologie»; «Variétés Kählériennes» and «Exposés sur les espaces homogènes
symétriques». Koszul visits to Brazil have been co-organized with a first visit to USP
in 1956 to give a course in August and September (lecture notes taken by José
de Barros Neto) on “Faisceaux et cohomologie” (general treatise on Cech cohomology with coefficients on a sheaf), published in 1957. A 2nd Course was given
in September and October of 1956 (lecture notes taken by Chaim Samuel Honig
and Carlos Benjamin de Lyra) on “Variétés Kâhlériennes”, published in 1957, and
also course on Multilinear Algebra, with notes by L. H. Jacy Monteiro, published in
1956. Last course on “Exposés sur les espaces homogènes symétriques ” was given
in September and October of 1958 with lecture notes published in 1959. R. Bott
commented on these seminars “very pleasant. The pace is fast, and the considerable material is covered elegantly. In addition to the more or less standard theorems
on symmetric spaces, the author discusses the geometry of geodesics, Bergmann’s
metrics, and finally studies the bounded domains with many details”.
Elected to Academia de Ciencias do Estado de Sao Paulo in 1981, Jean-Louis
Koszul visited USP again in 1986 for an inaugural talk at Instituto de Estudos
Avançados, hosted by A.A. M. Rodrigues on “The genesis of Bourbaki” (Fig. 5.2).
In the book “Selected papers of JL Koszul” [57], Koszul summarizes the work,
I will detail in the following: “It is with the problem of the determination of the
homogeneous bounded domains posed by E. Cartan around 1935 that are related
[my papers]. The idea of approaching the question through invariant Hermitian
forms already appears explicitly in Cartan. This leads to an algebraic approach
which constitutes the essence of Cartan’s work and which, with the Lie J-algebras,