Geometry of Derivation with Applications

<p><em><strong>Geometry of Derivation with Applications</strong></em> is the fifth work in a longstanding series of books on combinatorial geometry (<em>Subplane Covered Nets</em><em> Foundations of Translation Planes</em><em> Handbook of Finite Translation Planes</em> and <em>Combinatorics of Spreads and Parallelisms</em>). Like its predecessors this book will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases. Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume while ideas of non-commutative algebra are also described in detail with all the necessary background given a geometric treatment.</p><p>The book builds upon over twenty years of work concerning combinatorial geometry charted across four previous books and is suitable as a reference text for graduate students and researchers. It contains a variety of new ideas and generalizations of established work in finite affine geometry and is replete with examples and applications.</p>