Simple multilinear algebras and hermitian operators

T. S. R. Fuad; Jon D. Phillips; Xiaorong Shen; Jonathan D. H. Smith

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 2, page 251-259
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Fuad, T. S. R., et al. "Simple multilinear algebras and hermitian operators." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 251-259. <http://eudml.org/doc/248600>.

@article{Fuad2000,
abstract = {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.},
author = {Fuad, T. S. R., Phillips, Jon D., Shen, Xiaorong, Smith, Jonathan D. H.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {comtrans algebras; $T$-Hermitian matrices; simple algebras; comtrans algebra; Hermitian matrix; simple algebra},
language = {eng},
number = {2},
pages = {251-259},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Simple multilinear algebras and hermitian operators},
url = {http://eudml.org/doc/248600},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Fuad, T. S. R.
AU - Phillips, Jon D.
AU - Shen, Xiaorong
AU - Smith, Jonathan D. H.
TI - Simple multilinear algebras and hermitian operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 2
SP - 251
EP - 259
AB - 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.
LA - eng
KW - comtrans algebras; $T$-Hermitian matrices; simple algebras; comtrans algebra; Hermitian matrix; simple algebra
UR - http://eudml.org/doc/248600
ER -

References

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  1. Chein O., Pflugfelder H.O., Smith J.D.H., Quasigroups and Loops: Theory and Applications, Heldermann, Berlin, 1990. Zbl0719.20036MR1125806
  2. Goldberg V.V., Theory of Multicodimensional ( n + 1 ) -Webs, Kluwer, Dordrecht, 1988. Zbl0668.53001MR0998774
  3. Dirac P.A.M., The Principles of Quantum Mechanics, Oxford, 1967. MR0023198
  4. Saizew G.A., Algebraic Problems of Mathematical and Theoretical Physics (in Russian), Moscow, 1974; German translation: Berlin, 1979. MR0554236
  5. Shen X.R., Smith J.D.H., Simple multilinear algebras, rectangular matrices and Lie algebras, J. Algebra 160 (1993), 424-433. (1993) Zbl0811.17024MR1244921
  6. Shen X.R., Smith J.D.H., Comtrans algebras and bilinear forms, Arch. Math 59 (1992), 327-333. (1992) Zbl0739.17010MR1179457
  7. Shen X.R., Smith J.D.H., Representation theorem of comtrans algebras, J. Pure Appl. Algebra 80 (1992), 177-195. (1992) MR1172725
  8. Shen X.R., Smith J.D.H., Simple algebras of hermitian operators, Arch. Math. 65 (1995), 534-539. (1995) Zbl0853.17021MR1360074
  9. Smith J.D.H., Multilinear algebras and Lie's Theorem for formal n-loops, Arch. Math. 51 (1988), 169-177. (1988) Zbl0627.22003MR0959394
  10. Smith J.D.H., Comtrans algebras and their physical applications, Banach Center Publ. 28 (1993), 319-326. (1993) Zbl0811.17025MR1446291

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