الصفحة 1
الصفحة 1
Introduction to Lie Algebras
This book provides an elementary introduction to Lie algebras. It starts with basic concepts. A section on low-dimensional Lie algebras provides readers with experience of some useful examples. This is followed by a discussion of solvable Lie algebras and a strategy towards a classification of finite-dimensional complex Lie algebras. The next chapters cover Engel's theorem, Lie's theorem and Cartan's criteria and introduce some representation theory. The root-space decomposition of a semisimple Lie algebra is discussed, and the classical Lie algebras studied in detail. The authors also classify root systems, and give an outline of Serre's construction of complex semisimple Lie algebras. An overview of further directions then concludes the book and shows the high degree to which Lie algebras influence present-day mathematics.The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality.
Functional Identities
The theory of functional identities (FIs) is a relatively new one - the first results were published at the beginning of the 1990s, and this is the first book on this subject. An FI can be informally described as an identical relation involving arbitrary elements in an associative ring together with arbitrary (unknown) functions. The goal of the general FI theory is to describe these functions, or, when this is not possible, to describe the structure of the ring admitting the FI in question. This abstract theory has turned out to be a powerful tool for solving a variety of problems in ring theory, Lie algebras, Jordan algebras, linear algebra, and operator theory.
Function algebras on finite sets : Basic course on many-valued logic and clone theory
Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied. This book gives a broad introduction to the theory of function algebras and leads to the cutting edge of research. To familiarize the reader from the very beginning on with the algebraic side of function algebras the more general concepts of the Universal Algebra is given in the first part of the book. The second part on fuction algebras covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, clone theory.
Basic Notions of Algebra
Aims to present a general survey of algebra, of its basic notions and main branches.Those parts of the book devoted to the systematic treatment of notions and results of algebra make very limited demands on the reader: we presuppose only that the reader knows calculus, analytic geometry and linear algebra in the form taught in many high schools and colleges. The extent of the prerequisites required in our treatment of examples is harder to state; an acquaintance with projective space, topological spaces, differentiable and complex analytic manifolds and the basic theory of functions of a complex variable is desirable, but the reader should bear in mind that difficulties arising in the treatment of some specific example are likely to be purely local in nature, and not to affect the understanding of the rest of the book.
