SPENCER OPERATOR AND MACAULAY INVERSE SYSTEM : A New Approach to Control Identifiability and Other Engineering Applications.

Jean-François Pommaret (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

The Spencer operator, introduced by D.C. Spencer fifty years ago, is rarely used in mathematics today and, up to our knowledge, has never been used in engineering applications or mathematical physics. The purpose of this survey lecture at the second workshop on Differential Equations by Algebraic Methods (DEAM2, february 9-11, 2011, Linz, Austria) is to prove that the use of the Spencer operator constitutes the common secret of the three following famous books published about at the same time in the beginning of the last century, though they do not seem to have anything in common at first sight as they are successively dealing with elasticity theory, commutative algebra, electromagnetism and general relativity: 1) E. and F. COSSERAT: "Théorie des Corps Déformables", Hermann, Paris, 1909. 2) F.S. MACAULAY: "The Algebraic Theory of Modular Systems", Cambridge University Press, 1916. 3) H. WEYL: "Space, Time, Matter", Springer, Berlin, 1918 (1922, 1958; Dover, 1952).

Mots clés: Gauge theory; Spencer operator; Spencer sequence; Differential module; Macaulay inverse system; Socle; Top; Purity filtration; Cosserat equations; Weyl equations; Gauge theory.

Domaines: Equations aux dérivées partielles [math.AP]; Algèbre commutative [math.AC]; Géométrie différentielle [math.DG]; Théorie des groupes [math.GR]; Physique mathématique [math-ph]; Automatique / Robotique; Mécanique [physics.med-ph]; Electromagnétisme

Jean-François Pommaret. SPENCER OPERATOR AND MACAULAY INVERSE SYSTEM : A New Approach to Control Identifiability and Other Engineering Applications.. 2011. ⟨hal-00568937v1⟩