LEADER 04584nam 2200421 450 001 9910583033903321 005 20180801110541.0 010 $a0-12-814274-X 035 $a(CKB)4340000000209373 035 $a(MiAaPQ)EBC5108195 035 $a(PPN)226416313 035 $a(EXLCZ)994340000000209373 100 $a20171120h20182018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aWriting small omegas $eelie cartan's contributions to the theory of continuous groups 1894-1926 /$fAlberto Cogliati 205 $aFirst edition. 210 1$aLondon, England :$cAcademic Press,$d2018. 210 4$dİ2018 215 $a1 online resource (99 pages) 311 $a0-12-814244-8 320 $aIncludes bibliographical references. 327 $aMachine generated contents note:$g1.$tLie on the Backstage --$g1.1.$tFundamentals of Lie Theory of Finite Continuous Groups --$g1.1.1.$tThree Fundamental Theorems --$g1.1.2.$tThe Adjoint Croup --$g1.2.$t"A Fundamental Discipline" --$g2.$tCartan's Doctoral Dissertation --$g2.1.$tFinite Continuous Croups --$g2.1.1.$tReduced Form of a Given Group --$g2.1.2.$tSolvability and Semisimplicity Criteria --$g2.1.3.$tRadical and Decomposition Theorems --$g2.2.$tLie Theory of Complete Systems --$g2.3.$tComplete Systems and Canonical Reduction --$g2.4.$tAppendix --$g3.$tInfinite Continuous Groups 1883 -- 1902 --$g3.1.$tLie's First Contributions --$g3.2.$tDifferential Invariants --$g3.3.$tEngel's Habilitationsschrift --$g3.4.$tFoundations of Infinite Continuous Groups --$g3.5.$tOn a Theorem by Engel --$g3.6.$tMedolaghi's Contributions --$g3.7.$tVessiot and His Memoire couronnee --$g4.$tExterior Differential Systems --$g4.1.$tSome Technical Preliminaries --$g4.2.$tThe State-of-the-Art in the Early 1890s --$g4.3.$tEngel's Invariants Theory of Pfaffian Systems --$g4.3.1.$tInvariant Correspondences --$g4.4.$tVon Weber's Contributions: 1898 -- 1900 --$g4.4.1.$tCharacter and Characteristic Transformations --$g4.4.2.$tPfaffian Systems of Character One --$g4.4.3.$tReducibility of a Pfaffian System to Its Normal Form --$g4.5.$tThe Foundations of the Exterior Differential Calculus --$g4.6.$tCartan's Theory of General Pfaffian Systems --$g4.6.1.$tGeometrical Representation --$g4.6.2.$tCauchy's First Theorem --$g4.6.3.$tGenre and Characters --$g4.6.4.$tCharacteristic Elements --$g4.6.5.$tPfaffian Systems of Character One, II --$g4.7.$tSome Final Remarks --$g5.$tCartan's Theory 1902 -- 1909 --$g5.1.$tOn the Genesis of the Theory --$g5.2.$tSome Examples --$g5.3.$tCartan's Theory --$g5.3.1.$tFirst Fundamental Theorem --$g5.3.2.$tSecond and Third Fundamental Theorems --$g5.4.$tSubgroups of a Given Continuous Group --$g5.5.$tSimple Infinite Continuous Groups --$g5.6.$tEssential and Inessential Invariants --$g5.7.$tSome Final Remarks --$g6.$tCartan as a Geometer --$g6.1.$tIntroduction --$g6.2.$tMaurer -- (Cotton) -- Cartan Forms --$g6.3.$tCartan's 1910 Paper --$g6.4.$tThe Generalization of the Notion of Space --$g6.5.$tCartan's Collaboration with Schouten --$g6.6.$tConcluding Remarks --$gA.$tPicard -- Vessiot Theory --$gB.$tThe Galois of His Generation --$gC.$tClifford's Parallelism --$gC.1.$tKlein's Zur Nicht-Euklidischen Geometrie --$gC.2.$tBianchi and Fubini --$gC.3.$tEnea Bortolotti. 330 $aWriting Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 provides a general account of Lie's theory of finite continuous groups, critically examining Cartan's doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters. It evaluates pioneering attempts to generalize Lie's classical ideas to the infinite-dimensional case in the works of Lie, Engel, Medolaghi and Vessiot. Within this context, Cartan's groundbreaking contributions in continuous group theory, particularly in his characteristic and unique recourse to exterior differential calculus, are introduced and discussed at length. The work concludes by discussing Cartan's contributions to the structural theory of infinite continuous groups, his method of moving frames, and the genesis of his geometrical theory of Lie groups.--$cSource other than Library of Congress. 606 $aMathematics$vTextbooks 615 0$aMathematics 676 $a510 700 $aCogliati$b Alberto$0866183 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910583033903321 996 $aWriting small omegas$91933225 997 $aUNINA