PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 68(82), pp. 6771 (2000) 

Differentiable functions in associative and alternative algebras and smooth surfaces in projective spaces over these algebras}Boris RosenfeldDepartment of Mathematics, Pennsylvania State University, University Park 16802, USAAbstract: 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. Classification (MSC2000): 17A99; 53A40 Full text of the article:
Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 6 Feb 2002.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
