Differentiable functions in associative and alternative algebras and smooth surfaces in projective spaces over these algebras
Publications de l'Institut Mathématique, _N_S_68 (2000) no. 82, p. 67
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
The following assertions are proved: (1) in simple noncommutative
associative and alternative algebras only linear functions $y=ax+b$ and
$y=xa+b$ have left and right derivatives, and (2) in the space over all
commutative associative algebras smooth $m$-surfaces (lines
for $m=1$) have tangent $m$-planes depending on the same number of
parameters as points in surfaces. In the spaces over simple
noncommutative associative and alternative algebras only $m$-planes
(straight lines for $m=1$) are smooth $m$-surfaces. In the spaces over
nonsemisimple noncommutative algebras smooth $m$-surfaces have tangent
$m$-planes depending on the number of parameters less than points in
surfaces.
@article{PIM_2000_N_S_68_82_a6,
author = {Boris A. Rosenfeld},
title = {Differentiable functions in associative and alternative algebras and smooth surfaces in projective spaces over these algebras},
journal = {Publications de l'Institut Math\'ematique},
pages = {67 },
publisher = {mathdoc},
volume = {_N_S_68},
number = {82},
year = {2000},
zbl = {1058.53013},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a6/}
}
TY - JOUR AU - Boris A. Rosenfeld TI - Differentiable functions in associative and alternative algebras and smooth surfaces in projective spaces over these algebras JO - Publications de l'Institut Mathématique PY - 2000 SP - 67 VL - _N_S_68 IS - 82 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a6/ LA - en ID - PIM_2000_N_S_68_82_a6 ER -
%0 Journal Article %A Boris A. Rosenfeld %T Differentiable functions in associative and alternative algebras and smooth surfaces in projective spaces over these algebras %J Publications de l'Institut Mathématique %D 2000 %P 67 %V _N_S_68 %N 82 %I mathdoc %U http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a6/ %G en %F PIM_2000_N_S_68_82_a6
Boris A. Rosenfeld. Differentiable functions in associative and alternative algebras and smooth surfaces in projective spaces over these algebras. Publications de l'Institut Mathématique, _N_S_68 (2000) no. 82, p. 67 . http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a6/