04109nam 2200661 450 991081722610332120170821171534.01-4704-0633-0(CKB)3360000000464413(EBL)3113665(SSID)ssj0000973832(PQKBManifestationID)11612099(PQKBTitleCode)TC0000973832(PQKBWorkID)10989006(PQKB)11450925(MiAaPQ)EBC3113665(RPAM)2282074(PPN)195411129(EXLCZ)99336000000046441319800102h19801980 uy| 0engur|n|---|||||txtccrPseudo-riemannian symmetric spaces /M. Cahen, M. ParkerProvidence, Rhode Island :American Mathematical Society,[1980]©19801 online resource (119 p.)Memoirs of the American Mathematical Society ;number 229"Volume 24, number 229 (end of volume)."0-8218-2229-2 Bibliography: pages 107-108.""Table of Contents""; ""Introduction""; ""Chapter I. Pseudo-riemannian and pseudo-hermitian symmetric spaces""; ""Â 1. Pseudo-riemannian symmetric spaces""; ""Â 2. Pseudo-riemannian symmetric triples""; ""Â 3. Covering of symmetric spaces""; ""Â 4. Holonomy and the de Rham decomposition""; ""Â 5. Levi decomposition and reducibility""; ""Â 6. Pseudo-hermitian symmetric spaces""; ""Â 7. Levi factors""; ""Chapter II. Weakly irreducible spaces on which the action of the holonomy group is neither semi simple nor nilpotent""; ""Â 1. Decomposition of G into a direct sum of S-modules""""Â 2. Geometrical characterization of the subspaces X, P[sub(R)] and P[sub(S)]""""Â 3. Structure theorem for indecomposable PHSQ""; ""Â 4. Decomposition of V into minimal S-Ï?-stable subspaces""; ""Chapter III. Structure of the spaces admitting a maximal parallel foliation with zero curvature""; ""Â 1. Algebras with minimal multiplication""; ""Â 2. Construction of PRST and PHSQ with minimal multiplication""; ""Â 3. Classification of PRST with minimal multiplication""; ""Â 4. Symmetric spaces with parallel distribution""; ""Chapter IV. Structure of the S-module Y""""Â 1. Real and complex representations""""Â 2. Orthogonal representations""; ""Â 3. Representations compatible with Ï?""; ""Â 4. Non singular S-irreducible subspaces V[sub(Ï?)]""; ""Â 5. Non singular S-reducible subspaces V[sub(Ï?)]""; ""Â 6. Totally isotropic subspaces V[sub(Ï?)] in duality""; ""Â 7. Ricci tensor and complex structure""; ""Chapter V. Construction of the admissible S-modules V[sub(Ï?)]""; ""Â 1. Reformulation of the conditions of chapter IV""; ""Â 2. Some examples""; ""Â 3. Classification of the S-modules with dim S = 3""""Chapter VI. Some examples of non minimal multiplication""""Â 1. Indecomposable PRST with Levi factor Sl(2,R)/R""; ""Â 2. Indecomposable PHSQ with Levi factor Sl(2,R)/So(2) or So(3)/'So{2)""; ""Chapter VII. Classification of the indecomposable PRST of dimension lower than 8""; ""Â 1. Preliminary lemmas""; ""Â 2. dim P = 4""; ""Â 3. dim P = 5""; ""Â 4. dim P = 6""; ""Â 5. dim P = 7""; ""Bibliography""Memoirs of the American Mathematical Society ;no. 229.Symmetric spacesHermitian structuresHolonomy groupsRepresentations of algebrasLie algebrasSymmetric spaces.Hermitian structures.Holonomy groups.Representations of algebras.Lie algebras.516.3/62Cahen M(Michel),1935-1639128Parker M(Monique),1939-MiAaPQMiAaPQMiAaPQBOOK9910817226103321Pseudo-riemannian symmetric spaces3981906UNINA