Prof. em. Dr. Holger P. Petersson

• Veröffentlichungen und Preprints / Publications and preprints

  (a) Neuere Veröffentlichungen / recent publications

  1. (with Skip Garibaldi und M.L. Racine) Albert algebras over commutative rings. New Mathematical Monographs, Cambridge University Press. To appear. download (PDF 4 MB)
  2. (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)
  3. Norm equivalences and ideals of composition algebras. Münster J. of Math. 14 (2021), 283-293. download (PDF 277 KB)
  4. A survey on Albert algebras. Transformation Groups 24 (1) (2019), 219-278. download (PDF 549 KB)
  5. 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)
  6. (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)
  7. (with B. Mühlherr and R.M. Weiss) Descent in buildings. Princeton University Press, pp. 316, Princeton, NJ, USA (2015).
  8. An embedding theorem for reduced Albert algebras over arbitrary fields. Communications in Algebra 43 (2015), 2062-2088. Download (PDF 400 KB)
  9. (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)
  10. Maximal subalgebras of octonions. J. of Pure Appl. Algebra 217 (2013), 1700-1701. Download (PDF 494 KB)
  11. (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)
  12. (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)
  13. (with S. Garibaldi) Groups of outer type $E_6$ with trivial Tits algebras. Transf. Groups 12 (3) (2007), 443-474. Download (PDF 315 KB)
  14. Cyclic compositions and trisotopies. J. of Algebra 307 (2007), 49-96. Download (PDF 341 KB)
  15. (with M. Scherer) The number of nonisomorphic two-dimensional algebras over a finite field. Result. Math. 45 (2004), 137-152. Download (PDF 173 KB)
  16. (with M. Hübner) Two-dimensional real division algebras revisited. Beiträge zur Algebra und Geometrie 45 (1) (2004), 29-36. Download (PDF 123 KB)
  17. 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

  1. Zur Theorie der Lie-Tripel-Algebren. Math. Z. 97 (1967), 1 - 15.
  2. Über den Wedderburnschen Struktursatz für Lie-Tripel-Algebren. Math. Z. 98 (1967), 104 - 118.
  3. Isotopisms of Jordan algebras. Proc. Amer. Math. Soc. 20 (2) (1969), 477 - 482.
  4. Eine Identität fünften Grades, der gewisse Isotope von Kompositionsalgebren genügen. Math. Z. 109 (1969), 217 - 238.
  5. Borel subalgebras of alternative and Jordan algebras. J. Algebra 16 (4) (1970), 541 - 560.
  6. Eine Bemerkung zu quadratischen Divisionsalgebren. Arch. Math. (Basel) 22 (1) (1971), 59 - 61.
  7. Quasi composition algebras. Abh. Math. Sem. Univ. Hamburg 35 (3/4) (1971), 215 - 222.
  8. Jordan-Divisionsalgebren und Bewertungen. Math. Ann. 202 (1973), 215 - 243.
  9. Lokal kompakte Jordan-Divisionsringe. Abh. Math. Sem. Univ. Hamburg 39 (1973), 164 - 179.
  10. Composition algebras over a field with a discrete valuation. J. Algebra 29 (3) (1974), 414 - 426.
  11. Reduced simple Jordan algebras of degree 3 over a field with a discrete valuation. Arch. Math. (Basel) 25 (1974), 593 - 597.
  12. Exceptional Jordan division algebras over a field with a discrete valuation. J. Reine Angew. Math. 274 / 275 (1975), 1 - 20.
  13. Zur Arithmetik der Jordan-Paare. Math. Z. 147 (1976), 139 - 161.
  14. Conjugacy of idempotents in Jordan pairs. Comm. Algebra 6 (7) (1978), 673 - 715.
  15. The isotopy problem for Jordan matrix algebras. Trans. Amer. Math. Soc. 244 (1978), 185 - 197.
  16. Reduced Jordan matrix algebras over complete local rings. Nederl. Akad. Wetensch. Proc. Ser. A 81 (1) (1978), 97 - 109.
  17. Classification of locally compact Jordan division rings. J. Algebra 58 (2) (1979), 350 - 360.
  18. On linear and quadratic Jordan division algebras. Math. Z. 177 (1981), 541 - 548.
  19. (with M. L. Racine) Radicals of Jordan algebras of degree 3. Colloq. Math. Soc. János Bolyai 38 (1982), 349 - 377.
  20. Generic reducing fields of Jordan pairs. Trans. Amer. Math. Soc. 285 (2) (1984), 825 - 843.
  21. (with M. L. Racine) Cubic subfields of exceptional simple Jordan algebras. Proc. Amer. Math. Soc. 91 (1) (1984), 31 - 36.
  22. (with M. L. Racine) Springer forms and the first Tits construction of exceptional Jordan division algebras. Manuscripta Math. 45 (1984), 249 - 272.
  23. (with M. L. Racine) A norm theorem for central simple algebras of degree 3. Arch. Math. (Basel) 42 (1984), 224 - 228.
  24. (with M. L. Racine) The toral Tits process of Jordan algebras. Abh. Math. Sem. Univ. Hamburg 54 (1984), 251 - 256.
  25. (with M. L. Racine) Jordan algebras of degree 3 and the Tits process. J. Algebra 98 (1) (1986), 211 - 243.
  26. (with M. L. Racine) Classification of algebras arising from the Tits process. J. Algebra 98 (1) (1986), 244 - 279.
  27. (with M. L. Racine) Pure and generic first Tits constructions of exceptional Jordan division algebras. Algebras Groups Geom. 3 (1986), 386 - 398.
  28. Valuations on composition algebras. Nova J. Algebra Geom. 1 (2) (1992), 125 - 131.
  29. (with J. C. Ferrar) Exceptional simple Jordan algebras and Galois cohomology. Arch. Math. (Basel) 61 (1993), 517 - 520.
  30. Composition algebras over algebraic curves of genus zero. Trans. Amer. Math. Soc. 337 (1) (1993), 473 - 493.
  31. (with M. L. Racine) On the invariants mod 2 of Albert algebras. J. Algebra 174 (1995), 1049 - 1072.
  32. (with M. L. Racine) Reduced models of Albert algebras. Math. Z. 223 (1996), 367 - 385.
  33. (with M. L. Racine) An elementary approach to the Serre-Rost invariant of Albert algebras. Indag. Math., N. S., 7 (3) (1996), 343 - 365.
  34. (with M. L. Racine) The Serre-Rost Invariant of Albert Algebras in Characteristic three. Indag. Math., N. S., 8 (4) (1997), 543 - 548.
  35. Albert division algebras in characteristic three contain cyclic cubic subfields. Arch. Math. (Basel). 72 (1999),40 - 42.
  36. Grids and the arithmetics of Jordan pairs. J. Algebra 213 (1999), 77 - 128.
  37. The Albert algebra of generic matrices. Comm. Algebra 27 (1999), 3703 - 3717.
  38. The classification of two-dimensional nonassociative algebras. Result. Math. 3 (2000), 120 - 154.
  39. (with M. L .Racine) Octonion algebras obtained from associative algebras with involution. Proc. Amer. Math. Soc. 130 (6) (2002), 1563 - 1572.
  40. The structure group of an alternative algebra. Abh. Math. Sem. Univ. Hamburg. 72 (2002), 165 - 186.
  41. (with M. Thakur) The etale Tits process of Jordan algebras revisited J. of Algebra 273 (1) (2004), 88-107.
  42. Structure Theorems for Jordan algebras of degree three over fields of arbitrary characteristic. Communications in Algebra 32 (3) (2004), 1019 - 1049.
  43. (with M. Hübner) Two-dimensional real division algebras revisited. Beiträge zur Algebra und Geometrie 45 (1) (2004), 49 - 56.
  44. (with M. Scherer) The number of nonisomorphic two-dimensional algebras over finite field. Result. Math. 45 (2004), 137 - 152.
  45. Cyclic compositions and trisotopies. J. of Algebra 307 (2007), 49-96.
  46. (with S. Garibaldi) Groups of outer type $E_6$ with trivial Tits algebras. Transf. Groups 12 (3) (2007), 443-474.
  47. (with O. Loos und M.L. Racine) Inner derivations of alternative algebras over commutative rings. Algebra & Number Theory 2 (8) (2008), 927-968.
  48. (with S. Garibaldi) Wild Pfister forms over Henselian fields, K-theory and conic division algebras. J. of Algebra 327 (2011), 386-465.
  49. Maximal subalgebras of octonions. J. of Pure Appl. Algebra 217 (2013), 1700-1701.
  50. (witht J. Anquela und T. Cortes) Commuting U-operators in Jordan algebras. Trans. Amer. Math. Soc. 366 (2014), no.11, 5877-5902.
  51. An embedding theorem for reduced Albert algebras over arbitrary fields. Communications in Algebra 43 (2015), 2062-2088.
  52. (with B. Mühlherr und R. Weiss) Descent in buildings. Princeton University Press, pp. 316, Princeton, NJ, USA (2015.
  53. (with S. Garibaldi) Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras. Documenta Math. 21 (2016), 917-954.
  54. 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

  1. (with M. L. Racine) Exceptional Jordan division algebras. Contemporary Math. 13 (1982), 307 - 316.
  2. Compositional algebras over the projective line. Contemporary Math. 131 (1992), 673 - 678.
  3. 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.
  4. (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.
  5. (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.
  6. 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.
  7. 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

  1. (with A. Krieg) Max Koecher zum Gedächtnis. Jahresber. Deutsch. Math. Verein. 95 (1993), 1 - 27.
  2. Mathematik-Unterricht auf der Schule: Anspruch und Wirklichkeit. Hagener Universitäsreden.
  3. Der Pythagoräische Lehrsatz und seine Bedeutung für die geschichtliche Entwicklung der Mathematik. Hagener Universitätsreden, 25 (7) (1999), 5 - 25.
  4. H₃O - ein Kind der Quantenmechanik und der Algebra. Hagener Universitätsreden, 29 (1998), 27 - 37.

  (e) Preprints

  1. An observation on real division algebras, 2005. Download (PDF 61 KB)
  2. Completions of Jordan division algebras of degree 3 over fields with a discrete valuation, 2006. Download (PDF 100 KB)
  3. Idempotent 2-by-2 matrices, 2007. Download (PDF 207 KB)
  4. Polar decompositions of quaternion algebras over arbitrary rings, 2008. Download (PDF 170 KB)
  5. On a class of exotic cubic polynomial laws, 2010. Download (PDF 173 KB)
  6. Intervall decompositions on vector spaces over arbitrary fields, 2010. Download (PDF 182 KB)
  7. Albert algebras arising from central simple quartic Jordan algebras are reduced, 2012. Download (PDF 134 KB)
  8. The Dickson condition for conic algebras, 2012 Download (PDF 175 KB)

• Vorträge / lectures

  • 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, 69^th 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)