Simple multilinear algebras and hermitian operators
Fuad, T. S. R. ; Phillips, Jon D. ; Shen, Xiaorong ; Smith, Jonathan D. H.
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 251-259 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2000-01-01
Classification:  15A69,  17A40 
@article{119161,
     author = {T. S. R. Fuad and Jon D. Phillips and Xiaorong Shen and Jonathan D. H. Smith},
     title = {Simple multilinear algebras and hermitian operators},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {251-259},
     zbl = {1037.17005},
     mrnumber = {1780869},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119161}
}

Fuad, T. S. R.; Phillips, Jon D.; Shen, Xiaorong; Smith, Jonathan D. H. Simple multilinear algebras and hermitian operators. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 251-259. http://gdmltest.u-ga.fr/item/119161/

Chein O.; Pflugfelder H.O.; Smith J.D.H. Quasigroups and Loops: Theory and Applications, Heldermann, Berlin, 1990. | MR 1125806 | Zbl 0719.20036

Goldberg V.V. Theory of Multicodimensional $(n+1)$-Webs, Kluwer, Dordrecht, 1988. | MR 0998774 | Zbl 0668.53001

Dirac P.A.M. The Principles of Quantum Mechanics, Oxford, 1967. | MR 0023198

Saizew G.A. Algebraic Problems of Mathematical and Theoretical Physics (in Russian), Moscow, 1974; German translation: Berlin, 1979. | MR 0554236

Shen X.R.; Smith J.D.H. Simple multilinear algebras, rectangular matrices and Lie algebras, J. Algebra 160 (1993), 424-433. (1993) | MR 1244921 | Zbl 0811.17024

Shen X.R.; Smith J.D.H. Comtrans algebras and bilinear forms, Arch. Math 59 (1992), 327-333. (1992) | MR 1179457 | Zbl 0739.17010

Shen X.R.; Smith J.D.H. Representation theorem of comtrans algebras, J. Pure Appl. Algebra 80 (1992), 177-195. (1992) | MR 1172725

Shen X.R.; Smith J.D.H. Simple algebras of hermitian operators, Arch. Math. 65 (1995), 534-539. (1995) | MR 1360074 | Zbl 0853.17021

Smith J.D.H. Multilinear algebras and Lie's Theorem for formal n-loops, Arch. Math. 51 (1988), 169-177. (1988) | MR 0959394 | Zbl 0627.22003

Smith J.D.H. Comtrans algebras and their physical applications, Banach Center Publ. 28 (1993), 319-326. (1993) | MR 1446291 | Zbl 0811.17025