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Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces [[electronic resource] /] / by Marek Golasiński, Juno Mukai
| Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces [[electronic resource] /] / by Marek Golasiński, Juno Mukai |
| Autore | Golasiński Marek |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (148 p.) |
| Disciplina |
510
512.6 516.1 516.36 |
| Soggetto topico |
Convex geometry
Discrete geometry Differential geometry Category theory (Mathematics) Homological algebra Convex and Discrete Geometry Differential Geometry Category Theory, Homological Algebra |
| ISBN | 3-319-11517-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Gottlieb groups of Spheres -- Gottlieb and Whitehead Center Groups of Projective Spaces -- Gottlieb and Whitehead Center Groups of Moore Spaces. |
| Record Nr. | UNINA-9910299971003321 |
Golasiński Marek
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Grassmann and Stiefel Varieties over Composition Algebras [[electronic resource] /] / by Marek Golasiński, Francisco Gómez Ruiz
| Grassmann and Stiefel Varieties over Composition Algebras [[electronic resource] /] / by Marek Golasiński, Francisco Gómez Ruiz |
| Autore | Golasiński Marek |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (342 pages) |
| Disciplina | 514.34 |
| Altri autori (Persone) | Gómez RuizFrancisco |
| Collana | RSME Springer Series |
| Soggetto topico |
Geometry, Differential
Differential Geometry |
| ISBN | 3-031-36405-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- About the Book -- Contents -- 1 Algebraic Preliminaries -- 1.1 K-Algebras with Involutions: Composition K-Algebras -- 1.2 Generalized Frobenius-Hurwitz's Theorem -- 1.3 Matrices over K-Algebras -- Hermitian and Symmetric Matrices -- Trace -- Inner Products on M(A) -- General Linear Group -- Unitary Matrices -- Gram-Schmidt Orthonormalization Process -- Orientation on Vector Spaces -- Diagonalization of Hermitian Matrices -- Rank of a Matrix -- Idempotent Matrices -- 1.4 Background on Algebraic Geometry -- 1.5 Natural, Order and Zariski Topologies on M(A) -- The Natural Topology on M(A) -- The Order Topology on M(A) -- The Zariski Topology on M(A) -- 2 Exceptional Groups G2(K) and F4(K) -- 2.1 Cross Products and the Exceptional Group G2(K) -- Cross Product in Ln -- Properties -- The Group Aut(Ln,n-1) -- Cross Product in K3 -- Cross Product in C(K)n -- Cross Product in C(K)3 -- Cross Product in K7 -- The Group G2(K) -- Automorphisms of A -- Action of G2(K) on S6(K) -- Jordan Multiplication -- Automorphisms of M(A) -- 2.2 Automorphisms of Hermn(O(K)) -- The Canonical 3-form on the C(K)-Vector Space Sksymn(C(K)) -- Particular Case of n=3 -- 2.3 The Exceptional Group F4(K) -- Homogeneous Polynomials on Herm3(O(K)) -- Trace and Characteristic Coefficients -- Action of F4(K) on PK(Herm3(O(K)) -- Some Observations -- Further Observations -- A Canonical Inclusion of U3(H(K)) into F4(K) -- 3 Stiefel, Grassmann Manifolds and Generalizations -- 3.1 Stiefel Varieties -- 3.2 Grassmannians -- 3.3 Flag Varieties -- 4 More Classical Matrix Varieties -- 4.1 i-Grassmannians and i-Stiefel Varieties -- 4.2 i-Flag Varieties -- 5 Algebraic Generalizations of Matrix Varieties -- 5.1 Varieties of Idempotent Matrices -- Stiefel Varieties -- Tangent to Stiefel Varieties -- Normal to Stiefel varieties -- Grassmann Varieties -- The Stiefel Map.
Grassmannians as Homogeneous Spaces -- Tangent and Normal to Grassmannian Varieties -- Grassmann Varieties over K-Octonions -- Particular Cases -- A Canonical Decomposition for Matrices in Herm3(O(K)) -- Properties -- A Polynomial Inclusion S8(K) -3mu→(F4(K))E11 -- Flag Varieties -- Stiefel Maps over Flag Varieties -- Flag Varieties as Homogeneous Spaces -- i-Grassmann and i-Stiefel Varieties -- i-Stiefel Maps -- i-Grassmannians as Homogeneous Spaces -- i-Flag Varieties -- i-Stiefel Maps -- i-Flags Varieties as Homogeneous Spaces -- The Shuffle Product -- Idempotent Maps Representing the Tangent Bundles to (A), V(A), Idem(A) and G(A) -- 5.2 Atlas on Varieties of Matrices -- Some Zariski Closed Subsets of M(A) -- Atlas in Idem-,r(A) -- Another Atlas in Idem-,r(A) -- Atlas in G-,r(A) -- Another Atlas in G-,r(A) -- Hermitian Metric on G(C(K)) -- 6 Curvature, Geodesics and Distance on Matrix Varieties -- 6.1 The Stiefel Submersion -- 6.2 Curvatures -- 6.3 Ricci Tensor and Einstein Structures -- 6.4 Geodesics of G(A) and Idem(A) -- 6.5 Volume of Gn,r(A) -- 6.6 Riemannian Geometry of the Cayley Plane -- 6.7 Ricci Tensor and Einstein Structure of the Cayley Plane -- 6.8 Volume of the Cayley Plane -- A Definitions and Notations -- A.1 Multiplication Table in O(K) -- A.2 Matrices -- A.3 A,m,n-Operations -- A.4 Hermitian and Skew-Hermitian Matrices -- A.5 Trace -- A.6 Inner Product on M(A) -- A.7 Rank of a Matrix -- A.8 Groups of Matrices -- A.9 Classical Notations -- A.10 Group Monomorphisms -- A.11 Stiefel Varieties -- A.12 Non-compact Stiefel Varieties -- A.13 Grassmann Varieties (Classical) -- A.14 Grassmann Varieties -- A.15 Stiefel Maps -- A.16 Stiefel Varieties as Homogenous Spaces -- A.17 Grassmann Varieties as Homogenous Spaces -- A.18 Flag Varieties (Classical) -- A.19 Flag Varieties -- A.20 Stiefel Maps Over Flag Varieties. A.21 i-Grassmann Varieties (Classical) -- A.22 i-Grassmann Varieties -- A.23 i-Stiefel Varieties -- A.24 i-Stiefel Maps -- A.25 i-Stiefel Varieties as Homogenous Spaces -- A.26 i-Grassmann Varieties as Homogenous Spaces -- A.27 i-Flag Varieties -- A.28 Dimensions -- A.29 Tangents and Normals -- References -- Index. |
| Record Nr. | UNINA-9910739476003321 |
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Golasiński Marek
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| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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