| Title:
|
Simple multilinear algebras and hermitian operators (English) |
| Author:
|
Fuad, T. S. R. |
| Author:
|
Phillips, J. D. |
| Author:
|
Shen, X. R. |
| Author:
|
Smith, J. D. H. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
251-259 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper studies multilinear algebras, known as comtrans algebras, that are determined by so-called $T$-Hermitian matrices over an arbitrary field. The main result of this paper shows that the comtrans algebra of $n$-dimensional $T$-Hermitian matrices furnishes a simple comtrans algebra. (English) |
| Keyword:
|
comtrans algebras |
| Keyword:
|
$T$-Hermitian matrices |
| Keyword:
|
simple algebras |
| MSC:
|
15A69 |
| MSC:
|
17A40 |
| idZBL:
|
Zbl 1037.17005 |
| idMR:
|
MR1780869 |
| . |
| Date available:
|
2009-01-08T19:00:54Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119161 |
| . |
| Reference:
|
[1] Chein O., Pflugfelder H.O., Smith J.D.H.: Quasigroups and Loops: Theory and Applications.Heldermann, Berlin, 1990. Zbl 0719.20036, MR 1125806 |
| Reference:
|
[2] Goldberg V.V.: Theory of Multicodimensional $(n+1)$-Webs.Kluwer, Dordrecht, 1988. Zbl 0668.53001, MR 0998774 |
| Reference:
|
[3] Dirac P.A.M.: The Principles of Quantum Mechanics.Oxford, 1967. MR 0023198 |
| Reference:
|
[4] Saizew G.A.: Algebraic Problems of Mathematical and Theoretical Physics (in Russian).Moscow, 1974; German translation: Berlin, 1979. MR 0554236 |
| Reference:
|
[5] Shen X.R., Smith J.D.H.: Simple multilinear algebras, rectangular matrices and Lie algebras.J. Algebra 160 (1993), 424-433. Zbl 0811.17024, MR 1244921 |
| Reference:
|
[6] Shen X.R., Smith J.D.H.: Comtrans algebras and bilinear forms.Arch. Math 59 (1992), 327-333. Zbl 0739.17010, MR 1179457 |
| Reference:
|
[7] Shen X.R., Smith J.D.H.: Representation theorem of comtrans algebras.J. Pure Appl. Algebra 80 (1992), 177-195. MR 1172725 |
| Reference:
|
[8] Shen X.R., Smith J.D.H.: Simple algebras of hermitian operators.Arch. Math. 65 (1995), 534-539. Zbl 0853.17021, MR 1360074 |
| Reference:
|
[9] Smith J.D.H.: Multilinear algebras and Lie's Theorem for formal n-loops.Arch. Math. 51 (1988), 169-177. Zbl 0627.22003, MR 0959394 |
| Reference:
|
[10] Smith J.D.H.: Comtrans algebras and their physical applications.Banach Center Publ. 28 (1993), 319-326. Zbl 0811.17025, MR 1446291 |
| . |
