Prof. em. Dr. Holger P. Petersson
Kontakt
E-Mail: holger.petersson
VITA
- Geboren 1939 in Hamburg
- 1959 -1965 Studium der Mathematik und Physik an den Universitäten Münster und München
- 1965 Promotion in Mathematik, Universität München
- 1966 -1968 Assistant Professor, Department of Mathematics, The University of Iowa, Iowa City, Iowa, USA
- 1968 -1969 Forschungsstipendium der DFG an der Universität München
- 1970 -1973 Wissenschaftlicher Assistent, Mathematisches Institut, Universität Münster
- 1971 Habilitation in Mathematik, Universität Münster
- 1973 - 1978 Wissenschaftlicher Rat und Professor für Mathematik, Universität Münster
- 1978 - 2004 Professor für Mathematik, Fernuniversität in Hagen
- Seit 2004 emeritiert
Mitgliedschaften in wissenschaftlichen Organisationen:
Forschungsschwerpunkte
Kompositionsalgebren und kubische Jordan-Algebren, nicht-assoziative Divisions-Algebren, quadratische Formen über Henselkörpern
Research interests
Composition algebras and cubic Jordan algebras, non-associative division algebras, quadratic forms over Henselian fields
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(a) Neuere Veröffentlichungen / recent publications
- (with Skip Garibaldi und M.L. Racine) Albert algebras over commutative rings. New Mathematical Monographs, Cambridge University Press. To appear. download (PDF 4 MB)
- (with Skip Garibaldi und M.L. Racine) Albert algebras over Z and other rings. Forum of Mathematics, Sigma (2023) 11e.18, 1-38. download (PDF 613 KB)
- Norm equivalences and ideals of composition algebras. Münster J. of Math. 14 (2021), 283-293. download (PDF 177 KB)
- A survey on Albert algebras. Transformation Groups 24 (1) (2019), 219-278. download (PDF 549 KB)
- The non-orthogonal Cayley-Dickson construction and the octonionic structure of the E8-lattice. J. of Algebra Appl. 16 (2017) (12), pp. 52. download (PDF 406 KB)
- (with S. Garibaldi) Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras. Documenta Math. 21 (2016), 917-954. Download (PDF 449 KB)
- (with B. Mühlherr and R.M. Weiss) Descent in buildings. Princeton University Press, pp. 316, Princeton, NJ, USA (2015).
- An embedding theorem for reduced Albert algebras over arbitrary fields. Communications in Algebra 43 (2015), 2062-2088. Download (PDF 400 KB)
- (with J. Anquela and T. Cortes) Commuting U-operators in Jordan algebras. Trans. Amer. Math. Soc. 366 (2014), no.11, 5877-5902. Download (PDF 390 KB)
- Maximal subalgebras of octonions. J. of Pure Appl. Algebra 217 (2013), 1700-1701. Download (PDF 494 KB)
- (with S. Garibaldi) Wild Pfister forms over Henselian fields, K-theory and conic division algebras. J. of Algebra 327 (2011), 386-465. Download (PDF 459 KB)
- (with O. Loos and M.L. Racine) Inner derivations of alternative algebras over commutative rings. Algebra & Number Theory 2 (8) (2008), 927-968. Download (PDF 354 KB)
- (with S. Garibaldi) Groups of outer type $E_6$ with trivial Tits algebras. Transf. Groups 12 (3) (2007), 443-474. Download (PDF 315 KB)
- Cyclic compositions and trisotopies. J. of Algebra 307 (2007), 49-96. Download (PDF 341 KB)
- (with M. Scherer) The number of nonisomorphic two-dimensional algebras over a finite field. Result. Math. 45 (2004), 137-152. Download (PDF 173 KB)
- (with M. Hübner) Two-dimensional real division algebras revisited. Beiträge zur Algebra und Geometrie 45 (1) (2004), 29-36. Download (PDF 123 KB)
- Structure theorems for Jordan algebras of degree 3 over fields of arbitrary characteristic. Comm. In Algebra 32 (3) (2004), 1019-1049. Download (PDF 321 KB)
(b) Vollständige Liste der Veröffentlichungen / complete list of publications
Zeitschriftenartikel / journal articles
- Zur Theorie der Lie-Tripel-Algebren. Math. Z. 97 (1967), 1 - 15.
- Über den Wedderburnschen Struktursatz für Lie-Tripel-Algebren. Math. Z. 98 (1967), 104 - 118.
- Isotopisms of Jordan algebras. Proc. Amer. Math. Soc. 20 (2) (1969), 477 - 482.
- Eine Identität fünften Grades, der gewisse Isotope von Kompositionsalgebren genügen. Math. Z. 109 (1969), 217 - 238.
- Borel subalgebras of alternative and Jordan algebras. J. Algebra 16 (4) (1970), 541 - 560.
- Eine Bemerkung zu quadratischen Divisionsalgebren. Arch. Math. (Basel) 22 (1) (1971), 59 - 61.
- Quasi composition algebras. Abh. Math. Sem. Univ. Hamburg 35 (3/4) (1971), 215 - 222.
- Jordan-Divisionsalgebren und Bewertungen. Math. Ann. 202 (1973), 215 - 243.
- Lokal kompakte Jordan-Divisionsringe. Abh. Math. Sem. Univ. Hamburg 39 (1973), 164 - 179.
- Composition algebras over a field with a discrete valuation. J. Algebra 29 (3) (1974), 414 - 426.
- Reduced simple Jordan algebras of degree 3 over a field with a discrete valuation. Arch. Math. (Basel) 25 (1974), 593 - 597.
- Exceptional Jordan division algebras over a field with a discrete valuation. J. Reine Angew. Math. 274 / 275 (1975), 1 - 20.
- Zur Arithmetik der Jordan-Paare. Math. Z. 147 (1976), 139 - 161.
- Conjugacy of idempotents in Jordan pairs. Comm. Algebra 6 (7) (1978), 673 - 715.
- The isotopy problem for Jordan matrix algebras. Trans. Amer. Math. Soc. 244 (1978), 185 - 197.
- Reduced Jordan matrix algebras over complete local rings. Nederl. Akad. Wetensch. Proc. Ser. A 81 (1) (1978), 97 - 109.
- Classification of locally compact Jordan division rings. J. Algebra 58 (2) (1979), 350 - 360.
- On linear and quadratic Jordan division algebras. Math. Z. 177 (1981), 541 - 548.
- (with M. L. Racine) Radicals of Jordan algebras of degree 3. Colloq. Math. Soc. János Bolyai 38 (1982), 349 - 377.
- Generic reducing fields of Jordan pairs. Trans. Amer. Math. Soc. 285 (2) (1984), 825 - 843.
- (with M. L. Racine) Cubic subfields of exceptional simple Jordan algebras. Proc. Amer. Math. Soc. 91 (1) (1984), 31 - 36.
- (with M. L. Racine) Springer forms and the first Tits construction of exceptional Jordan division algebras. Manuscripta Math. 45 (1984), 249 - 272.
- (with M. L. Racine) A norm theorem for central simple algebras of degree 3. Arch. Math. (Basel) 42 (1984), 224 - 228.
- (with M. L. Racine) The toral Tits process of Jordan algebras. Abh. Math. Sem. Univ. Hamburg 54 (1984), 251 - 256.
- (with M. L. Racine) Jordan algebras of degree 3 and the Tits process. J. Algebra 98 (1) (1986), 211 - 243.
- (with M. L. Racine) Classification of algebras arising from the Tits process. J. Algebra 98 (1) (1986), 244 - 279.
- (with M. L. Racine) Pure and generic first Tits constructions of exceptional Jordan division algebras. Algebras Groups Geom. 3 (1986), 386 - 398.
- Valuations on composition algebras. Nova J. Algebra Geom. 1 (2) (1992), 125 - 131.
- (with J. C. Ferrar) Exceptional simple Jordan algebras and Galois cohomology. Arch. Math. (Basel) 61 (1993), 517 - 520.
- Composition algebras over algebraic curves of genus zero. Trans. Amer. Math. Soc. 337 (1) (1993), 473 - 493.
- (with M. L. Racine) On the invariants mod 2 of Albert algebras. J. Algebra 174 (1995), 1049 - 1072.
- (with M. L. Racine) Reduced models of Albert algebras. Math. Z. 223 (1996), 367 - 385.
- (with M. L. Racine) An elementary approach to the Serre-Rost invariant of Albert algebras. Indag. Math., N. S., 7 (3) (1996), 343 - 365.
- (with M. L. Racine) The Serre-Rost Invariant of Albert Algebras in Characteristic three. Indag. Math., N. S., 8 (4) (1997), 543 - 548.
- Albert division algebras in characteristic three contain cyclic cubic subfields. Arch. Math. (Basel). 72 (1999),40 - 42.
- Grids and the arithmetics of Jordan pairs. J. Algebra 213 (1999), 77 - 128.
- The Albert algebra of generic matrices. Comm. Algebra 27 (1999), 3703 - 3717.
- The classification of two-dimensional nonassociative algebras. Result. Math. 3 (2000), 120 - 154.
- (with M. L .Racine) Octonion algebras obtained from associative algebras with involution. Proc. Amer. Math. Soc. 130 (6) (2002), 1563 - 1572.
- The structure group of an alternative algebra. Abh. Math. Sem. Univ. Hamburg. 72 (2002), 165 - 186.
- (with M. Thakur) The etale Tits process of Jordan algebras revisited J. of Algebra 273 (1) (2004), 88-107.
- Structure Theorems for Jordan algebras of degree three over fields of arbitrary characteristic. Communications in Algebra 32 (3) (2004), 1019 - 1049.
- (with M. Hübner) Two-dimensional real division algebras revisited. Beiträge zur Algebra und Geometrie 45 (1) (2004), 49 - 56.
- (with M. Scherer) The number of nonisomorphic two-dimensional algebras over finite field. Result. Math. 45 (2004), 137 - 152.
- Cyclic compositions and trisotopies. J. of Algebra 307 (2007), 49-96.
- (with S. Garibaldi) Groups of outer type $E_6$ with trivial Tits algebras. Transf. Groups 12 (3) (2007), 443-474.
- (with O. Loos und M.L. Racine) Inner derivations of alternative algebras over commutative rings. Algebra & Number Theory 2 (8) (2008), 927-968.
- (with S. Garibaldi) Wild Pfister forms over Henselian fields, K-theory and conic division algebras. J. of Algebra 327 (2011), 386-465.
- Maximal subalgebras of octonions. J. of Pure Appl. Algebra 217 (2013), 1700-1701.
- (witht J. Anquela und T. Cortes) Commuting U-operators in Jordan algebras. Trans. Amer. Math. Soc. 366 (2014), no.11, 5877-5902.
- An embedding theorem for reduced Albert algebras over arbitrary fields. Communications in Algebra 43 (2015), 2062-2088.
- (with B. Mühlherr und R. Weiss) Descent in buildings. Princeton University Press, pp. 316, Princeton, NJ, USA (2015.
- (with S. Garibaldi) Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras. Documenta Math. 21 (2016), 917-954.
- The non-orthogonal Cayley-Dickson construction and the octonionic structure of the E8-lattice. To appear in J. of Algebra Appl.
(c) Konferenzberichte / conference reports
- (with M. L. Racine) Exceptional Jordan division algebras. Contemporary Math. 13 (1982), 307 - 316.
- Compositional algebras over the projective line. Contemporary Math. 131 (1992), 673 - 678.
- Max Koecher's work on Jordan algebras. In W. Kaup, K. McCrimmon, H. P. Petersson (eds.): Jordan Algebras, Conference Proceedings Oberwolfach 1992, 187 - 195. Berlin, New York: de Gruyter 1994.
- (with M. L. Racine) Albert Algebras In W. Kaup, K. McCrimmon, H. P. Petersson (eds.): Jordan Algebras, Conference Proceedings Oberwolfach 1992, 197 - 207. Berlin, New York: de Gruyter 1994.
- (with M. L. Racine) Enumeration and classification of Albert algebras: Reduced models and the invariants mod 2, In As. Gonzales (ed.): Non-associative algebra and its applications, 334 - 340. Dordrecht Boston London: Kluwer 1994.
- Problems and perspectives of teaching mathematics in distance education. In R. Bartz, G. Fandel, F. Nickolmann (eds,): University level distance education in Europe - Assessment and perspectives. Proceedings of a workshop by FernUniversität and EADTU in Hagen, December 2/3, 1994; 105 - 110. Weinheim: Deutscher Studienverlag 1996.
- Grids and the arithmetics of Jordan pairs. A. Castellón, J. Cuenze, A. Fernández, C. Martín (eds.): Proceedings of the International Conference on Jordan structures, Malaga, 1997.
(d) Miscellania
- (with A. Krieg) Max Koecher zum Gedächtnis. Jahresber. Deutsch. Math. Verein. 95 (1993), 1 - 27.
- Mathematik-Unterricht auf der Schule: Anspruch und Wirklichkeit. Hagener Universitäsreden.
- Der Pythagoräische Lehrsatz und seine Bedeutung für die geschichtliche Entwicklung der Mathematik. Hagener Universitätsreden, 25 (7) (1999), 5 - 25.
- H3O - ein Kind der Quantenmechanik und der Algebra. Hagener Universitätsreden, 29 (1998), 27 - 37.
(e) Preprints
- An observation on real division algebras, 2005. Download (PDF 61 KB)
- Completions of Jordan division algebras of degree 3 over fields with a discrete valuation, 2006. Download (PDF 100 KB)
- Idempotent 2-by-2 matrices, 2007. Download (PDF 207 KB)
- Polar decompositions of quaternion algebras over arbitrary rings, 2008. Download (PDF 170 KB)
- On a class of exotic cubic polynomial laws, 2010. Download (PDF 173 KB)
- Intervall decompositions on vector spaces over arbitrary fields, 2010. Download (PDF 182 KB)
- Albert algebras arising from central simple quartic Jordan algebras are reduced, 2012. Download (PDF 134 KB)
- The Dickson condition for conic algebras, 2012 Download (PDF 175 KB)
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- Integral octonions. Workshop on non-associative algebras, Malaga, 2018. Download (PDF 234 KB)
- An algebraic formalism for the octonionic structure of the E8 lattice. Conference in honor of Richard Weiss. Universität Karlsruhe 2016. Download (PDF 216 KB)
- Vektorprodukt und Graves-Cayley-Oktonionen. Fakultät für Mathematik und Informatik, Fernuniversität, 2015. Download (PDF 234 KB)
- Conic division algebras. Universidad de Oviedo, 2013. Download (PDF 267 KB)
- Anisotropic quadratic forms over local fields. Universidad de Malaga, 2013. Download (PDF 242 KB)
- Construction and classification of cubic Jordan algebras, mini-course 2012 on Galois cohomology motives and cubic Jordan algebras, Universite d'artois, Lens, 2012.
- Moufang sets and the problem of commuting U-operators, 69th Algebra Day, University of Ottawa, 2012.
- Moufang sets and the problem of commuting U-operators, Universidad Rey Juan Carlos, Madrid, 2011. Download (PDF 274 KB)
- Experiments in cubic systems, Universidad de Malaga, 2011. Download (PDF 222 KB)
- Pfister forms in characteristic 2, workshop, Universidad de Cordoba, 2009.
- Composition algebras over local fields revisited, workshop, University of Ottawa, 2008. Download (PDF 225 KB)
- Composition algebras over commutative rings, Conference on linear algebraic groups and cohomology, Emory University, 2007. Download (PDF 145 KB)
- Composition algebras over commutative rings, workshop, Universidad de Malaga, 2007.
Download (PDF 177 KB) - Co-ordinatizing Jordan algebras of degree three by means of cubic etale subalgebras, workshop, Universitay of Ottawa, 2005.
- The Skolem-Noether problem for Albert algebras, University of Nottingham, 2005.
Download (PDF 107 KB)
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| 12.09.2024