Geometry of derivation with applications. (2023)

• Record Type: Book
• Further Information: Note: Norman L. Johnson.
• Authors: Johnson, Norman Lloyd
• Contents: Contents Preface Part 1. Classical theory of derivation Chapter 1. Coordinate methods Translation planes and quasifibrations Quasifields Left quasifields T -extension Chapter 2. Embedding theory of derivable nets Co-dimension 2 construction Structure theory and contraction of embedded nets Embedding of subplane covered nets Transversals to derivable nets Part 2. Classifying derivable nets over skewfields Chapter 3. Fundamentals & background Uniform representation for quaternion division rings Quaternion division ring planes Matrices and determinants over skewfields Classifying derivable nets Chapter 4. Classification theory over skewfields Notation Extension of skewfields theorem/Skewfield bimodules Preliminary types 1, 2, 3 Standard framework Generalized quaternions over skewfields Matrix skewfields are generalized quaternion Generalized (a, b )F contains (a, b )Z (F ) Brauer groups Extending skewfields Part 3. Types i of derivable nets Chapter 5. The types CONTENTS Type 0 Double regulus type 0 derivable nets The ambient space Derivable nets of type 3 Order in type 3 derivable nets Derivable nets of type 2 Fake type 2 derivable nets Open form derivable nets of type 2 Order in type 2 derivable nets Derivable nets of type 1 Examples of type 1 derivable nets Carrier nets Derivable nets in translation planes Part 4. Flocks of a -cones Chapter 6. Klein quadric and generalization a -Klein quadric Construction of general flocks The field case Algebraic construction for a -cones Elation groups and flokki planes Maximal partial spreads and a -flokki The second cone Baer groups for flokki Planes q -Flokki and lifting Collineations and isomorphisms of a -flokki planes Part 5. Flock geometries Chapter 7. Related geometries Kantor's coset technique Quasi-BLT-sets s -Inversion & s -square A census Quasi-flock derivations Herds of Hyperovals Hyperbolic fibrations The correspondence theorem Flocks to cyclic planes. Part 6. Twisted hyperbolic flocks Chapter 8. Hyperbolic flocks and generalizations. Algebraic theory of twisted hyperbolic flocks Simultaneous a -Flocks & twisted hyperbolic spreads CONTENTS Flocks of D -cones j planes and twisted hyperbolic flocks Joint theory of a -flocks The Ka -Klein quadric Baer theory Quasi-flocks The Baer forms Algebraic and a -Klein methods Infinite flocks of hyperbolic quadrics Part 7. Lifting Chapter 9. Chains & surjectivity of degree 1 1. Restricted surjectivity 2. Hughes-Kleinfield look-alikes 3. The remaining quasifibrations of dimension 2 4. Large dimension quasifibrations 5. T -copies of generalized twisted field planes Part8. Lifting skewfields Chapter 10. General theory 1. Matrix forms and replacement 2. The general skewfield spread 3. Generalized quaternion division rings 4. Retraction Part 9.Bilinearity Chapter 11. General bilinear geometries Star flocks and rigidity Bilinear a -flocks Bilinear flocks of quadratic cones Translation planes admitting SL (2, K ) Double covers nm -Linear flocks of quadratic cones Nests of reguli Group replaceable translation planes Circle geometry over K (✓-- ) aa -1 -nest planes Flocks of elliptic quadrics Klein quadric and Pappian spreads n -Linear elliptic flocks Tangential packings of ovoids Part 10. Multiple replacement theorem Chapter 11. General bilinear geometries Star flocks and rigidity Bilinear a -flocks Bilinear flocks of quadratic cones Translation planes admitting SL (2, K ) Double covers nm -Linear flocks of quadratic cones Nests of reguli Group replaceable translation planes Circle geometry over K (✓-- ) aa -1 -nest planes Flocks of elli
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2023
• Extent: 1 online resource (393 pages)
• Subjects: 516.13; Combinatorial geometry
• Languages: English
• ISBNs: 9781000883886; 9781000883817
• Related ISBNs: 9781032349169
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
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