Lectures in Abstract Algebra: Linear Algebra, Vol. 2

Science & Math

Jacobson, Nathan

Mathematics

D. Van Nostrand Co., Inc.

Lectures in Abstract Algebra: Theory of Fields and Galois Theory v. 3 (The University Series in Higher Mathematics)

D. Van Nostrand and Company

Lie group theory, developed by M. Sophus Lie in the nineteenth century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a text for graduate courses. Chapter 1 introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Cartan’s criterion and its consequences, and split semi-simple Lie algebras. Chapter 5, on universal enveloping algebras, provides the abstract concepts underlying representation theory. The basic results on representation theory are given in three succeeding chapters: the theorem of Ado-Iwasawa, classification of irreducible modules, and characters of the irreducible modules. In Chapter 9 the automorphisms of semi-simple Lie algebras over an algebraically closed field of characteristic zero are determined. These results are applied in Chapter 10 to the problems of sorting out the simple Lie algebras over an arbitrary field. The reader, to fully benefit from this tenth chapter, should have some knowledge about the notions of Galois theory and some of the results of the Wedderburn structure theory of associative algebras. Nathan Jacobson, presently Henry Ford II Professor of Mathematics at Yale University, is a well-known authority in the field of abstract algebra. His book, Lie Algebras, is a classic handbook both for researchers and students. Though it presupposes knowledge of linear algebra, it is not overly theoretical and can be readily used for self-study.

Lie Algebras (Dover Books on Mathematics)

Dover Publications

Basic Algebra I

W.H.Freeman and Company

"These two volumes must be regarded as a landmark in algebraical literature. The enormous wealth of material, the depth of treatment, and the masterly exposition render these volumes exceptionally valuable. All courses on algebra, from the second undergraduate year to the specialist studies for doctoral students, can benefit from this authoritative treatise by Professor Jacobson." Walter Ledermann, University of Sussex Volume1

W.H.Freeman & Co.

A revision of the text for graduate students who have already taken a strong first course. As in "Basic Algebra I", this text is for students of mathematics in the broad sense, not just for specialists in algebra. It stresses important applications and concrete instances of theory. Historical notes show the student the continuity of algebra with its modern developments and the relation of the subject to other areas of mathematics.

Basic Algebra II

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Structure and Representations of Jordan Algebras (American Mathematical Society Colloquium Publications)

Amer Mathematical Society

Here, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.

Finite-Dimensional Division Algebras over Fields

Springer

Scorched Earth: The Cinder Chronicles

Science Fiction & Fantasy

Fantasy

Independently published

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