Vector product and composition algebras in braided monoidal additive categories

Ross Street

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 4, page 581-604
  • ISSN: 0010-2628

Abstract

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This is an account of some work of Markus Rost and his students Dominik Boos and Susanne Maurer. It concerns the possible dimensions for composition (also called Hurwitz) algebras. We adapt the work to the braided monoidal setting.

How to cite

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Street, Ross. "Vector product and composition algebras in braided monoidal additive categories." Commentationes Mathematicae Universitatis Carolinae 60.4 (2019): 581-604. <http://eudml.org/doc/295076>.

@article{Street2019,
abstract = {This is an account of some work of Markus Rost and his students Dominik Boos and Susanne Maurer. It concerns the possible dimensions for composition (also called Hurwitz) algebras. We adapt the work to the braided monoidal setting.},
author = {Street, Ross},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {string diagram; vector product; bilinear form; braiding; monoidal dual},
language = {eng},
number = {4},
pages = {581-604},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Vector product and composition algebras in braided monoidal additive categories},
url = {http://eudml.org/doc/295076},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Street, Ross
TI - Vector product and composition algebras in braided monoidal additive categories
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 4
SP - 581
EP - 604
AB - This is an account of some work of Markus Rost and his students Dominik Boos and Susanne Maurer. It concerns the possible dimensions for composition (also called Hurwitz) algebras. We adapt the work to the braided monoidal setting.
LA - eng
KW - string diagram; vector product; bilinear form; braiding; monoidal dual
UR - http://eudml.org/doc/295076
ER -

References

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  2. Boos D., Ein tensorkategorieller Zugang zum Satz von Hurwitz, Diplomarbeit ETH Zürich, Zürich, 1998 (Deutsch). 
  3. Hurwitz A., Über die Komposition der quadratischen Formen von beliebig vielen Variablen, Nachrichten Ges. der Wiss. Göttingen (1898), 309–316; in: Mathematische Werke. Bd. II, Zahlentheorie, Algebra und Geometrie, Birkhäuser, Basel, 1963, 565–571 (Deutsch). MR0154778
  4. Hurwitz A., 10.1007/BF01448439, Math. Ann. 88 (1922), no. 1–2, 1–25 (Deutsch). MR1512117DOI10.1007/BF01448439
  5. Joyal A., Street R., 10.1016/0001-8708(91)90003-P, Adv. Math. 88 (1991), no. 1, 55–112. MR1113284DOI10.1016/0001-8708(91)90003-P
  6. Joyal A., Street R., 10.1006/aima.1993.1055, Adv. Math. 102 (1993), no. 1, 20–78. MR1250465DOI10.1006/aima.1993.1055
  7. Mac Lane S., 10.1007/978-1-4612-9839-7, Graduate Texts in Mathematics, 5, Springer, New York, 1971. Zbl0906.18001MR1712872DOI10.1007/978-1-4612-9839-7
  8. Maurer S., Vektorproduktalgebren, Diplomarbeit Universität Regensburg, Regensburg, 1998 (Deutsch). 
  9. Rost M., On the dimension of a composition algebra, Doc. Math. 1 (1996), no. 10, 209–214. MR1397790
  10. Westbury B. W., Hurwitz' theorem on composition algebras, available at arXiv:1011.6197 [math.RA] (2010), 33 pages. 

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