[8 offprints, including:] On the Geometric Algebra of the Octave Planes.

8 offprints. Original wrappers. From the collection of Abraham Pais. Very good. INVENTORY: 1. SPRINGER, T. A. The Projective Octave Plane. Offprint from: "Algebraical and topological foundations of geometry." pp. 173-4. [Proceedings of a Colloquium Held in Utrecht, August 1959. Pergamon Press, 1962]. Abstract: "This chapter discusses the projective octave plane. Let a* be a line in Full-size image (3 K). On deleting a*, one gets an affine plane Full-size image (3 K) in Full-size image (3 K). One result of the analysis of the group of K-linear transformations of Full-size image (3 K) leaving the cubic form det invariant up to a scalar factor 0 and inducing in Full-size image (3 K) a collineation leaving a* invariant as a whole is that Full-size image (3 K) is a translation-plane, which means that for any two points b* and c* of Full-size image (3 K) there is a unique translation in Full-size image (3 K) sending b* into c*. This implies that Full-size image (3 K) is harmonic, that is, that for any three distinct collinear points, there is a unique fourth harmonic point, which may be constructed in the usual manner. As a consequence, one obtains the result that the collination-group of Full-size image (3 K) is isomorphic with the projective group of semi-linear transformations of A leaving det invariant up to a scalar factor 0." :: Proceedings of a Colloquium Held in Utrecht. 2. SPRINGER, T. A. On a Class of Jordan Algebras. Offprint from: Koninkl Nederl Akademie van Wetenschappen, series A, 62, no. 3 and Indag. Math., 21, no. 3, pp 254-264, 1959. 3. SPRINGER, T. A. The Projective Octave Plane. I. Offprint from: Koninkl Nederl Akademie van Wetenschappen, series A, 63, no. 1 and Indag. Math., 22, no. 1, pp. 74-101, 1960. 4. SPRINGER, T. A.; VAN DER BLIJ, F. Octaves and Triality. Offprint from: Nieuw Archief voor Wiskunde (3), VIII, pp. 158-169, 1960. 5. SPRINGER, T. A. The Classification of Reduced Exceptional Simple Jordan Algebras. Koninkl Nederl Akademie van Wetenschappen, series A, 63, no. 4 and Indag. Math., 22, no. 4, pp. 414-422, 1960. 6. SPRINGER, T. A. Characterization of a Class of Cubic Forms. Koninkl Nederl Akademie van Wetenschappen, series A, 65, no. 3, and Indag. Math., 24, no. 3, pp.259-265, 1962. 7. SPRINGER, T. A. On the Geometric Algebra of the Octave Planes. Koninkl Nederl Akademie van Wetenschappen, series A, 65, no. 4, and Indag. Math., 24, no. 4, pp. 451-468, 1962. 8. SPRINGER, T. A. Elliptic and Hyperbolic Octave Planes. I. Koninkl Nederl Akademie van Wetenschappen, series A, 66, no. 3, and Indag. Math., 25, no. 3, pp.413-451, 1963. There were additional parts II and III issued later, also in 1963. / Springer was a mathematician, studied at Leiden University, taking his PhD under Hendrik Kloosterman, did his post-doctorate work at University of Nancy before returning to Leiden, from 1955 we lectured at Utrecht University, becoming Professor of Mathematics ordinarius (1959-1991) :: then becoming professor emeritus. He was visiting professor in various places, including the Institute for Advanced Study, Princeton. Springer worked on linear algebraic groups, Hecke algebras, complex reflection groups, and who introduced Springer representations and the Springer resolution. "In 1976, Tonny Springer discovered the remarkable fact that the permutation group acts naturally on (the cohomology of) a collection of algebraic varieties, now called Springer fibers. Indeed, all of the irreducible representations - the building blocks of an arbitrary representation - can be constructed by examining the permutation action on a handful of these Springer fibers. Springer's original construction was completely algebraic but was followed by intense activity on the part of many people to give more intrinsically geometric explanations for these representations." See: J. J. O'Connor and E. F. Robertson, [biography]

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Publisher: Koninklijke Nederlandse Akademie van Wetenschappen, 1962.

Year: 1962

Type: Used

Binding: Softcover

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