| Title:
|
Vector product and composition algebras in braided monoidal additive categories (English) |
| Author:
|
Street, Ross |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
581-604 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
string diagram |
| Keyword:
|
vector product |
| Keyword:
|
bilinear form |
| Keyword:
|
braiding |
| Keyword:
|
monoidal dual |
| MSC:
|
11E20 |
| MSC:
|
15A03 |
| MSC:
|
17A75 |
| MSC:
|
18D10 |
| idZBL:
|
Zbl 07177891 |
| idMR:
|
MR4061364 |
| DOI:
|
10.14712/1213-7243.2019.024 |
| . |
| Date available:
|
2020-02-10T16:50:45Z |
| Last updated:
|
2022-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147978 |
| . |
| Reference:
|
[1] Baez J. C.: The octonions.Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 2, 45–205. Zbl 1026.17001, MR 1886087 |
| Reference:
|
[2] Boos D.: Ein tensorkategorieller Zugang zum Satz von Hurwitz.Diplomarbeit ETH Zürich, Zürich, 1998 (Deutsch). |
| Reference:
|
[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). MR 0154778 |
| Reference:
|
[4] Hurwitz A.: Über die Komposition der quadratischen Formen.Math. Ann. 88 (1922), no. 1–2, 1–25 (Deutsch). MR 1512117, 10.1007/BF01448439 |
| Reference:
|
[5] Joyal A., Street R.: The geometry of tensor calculus I.Adv. Math. 88 (1991), no. 1, 55–112. MR 1113284, 10.1016/0001-8708(91)90003-P |
| Reference:
|
[6] Joyal A., Street R.: Braided tensor categories.Adv. Math. 102 (1993), no. 1, 20–78. MR 1250465, 10.1006/aima.1993.1055 |
| Reference:
|
[7] Mac Lane S.: Categories for the Working Mathematician.Graduate Texts in Mathematics, 5, Springer, New York, 1971. Zbl 0906.18001, MR 1712872, 10.1007/978-1-4612-9839-7 |
| Reference:
|
[8] Maurer S.: Vektorproduktalgebren.Diplomarbeit Universität Regensburg, Regensburg, 1998 (Deutsch). |
| Reference:
|
[9] Rost M.: On the dimension of a composition algebra.Doc. Math. 1 (1996), no. 10, 209–214. MR 1397790 |
| Reference:
|
[10] Westbury B. W.: Hurwitz' theorem on composition algebras.available at arXiv:1011.6197 [math.RA] (2010), 33 pages. |
| . |
