Extending Structures

<p><strong><em>Extending Structures: Fundamentals and Applications</em></strong> treats the extending structures (ES) problem in the context of groups Lie/Leibniz algebras associative algebras and Poisson/Jacobi algebras. This concisely written monograph offers the reader an incursion into the extending structures problem which provides a common ground for studying both the extension problem and the factorization problem.</p><p>Features</p><ul> <p> </p> <li>Provides a unified approach to the extension problem and the factorization problem </li> <p> </p> <li>Introduces the classifying complements problem as a sort of converse of the factorization problem; and in the case of groups it leads to a theoretical formula for computing the number of types of isomorphisms of all groups of finite order that arise from a minimal set of data</li> <p> </p> <li>Describes a way of classifying a certain class of finite Lie/Leibniz/Poisson/Jacobi/associative algebras etc. using flag structures</li> <p> </p> <li>Introduces new (non)abelian cohomological objects for all of the aforementioned categories</li> <p> </p> <li>As an application to the approach used for dealing with the classification part of the ES problem the Galois groups associated with extensions of Lie algebras and associative algebras are described</li> </ul>