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
Cet article a éte moissonné depuis 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 },
year = {2000},
volume = {_N_S_68},
number = {82},
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 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 %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/