Books in the Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge series

[...] Springer's work will be of service to research workers familiar with linear algebraic groups who find they need to know something about Jordan algebras and will provide Jordan algebraists with new techniques and a new approach to finite-dimensional algebras over fields."

This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan.

This book is a study of group theoretical properties of two dis parate kinds, firstly finiteness conditions or generalizations of fini teness and secondly generalizations of solubility or nilpotence.

Generalized Nilpotent Groups.- Engel Groups.- Local Theorems and Generalized Soluble Groups.- Residually Finite Groups.- Some Topics in the Theory of Infinite Soluble Groups.

This book is a study of group theoretical properties of two dis parate kinds, firstly finiteness conditions or generalizations of fini teness and secondly generalizations of solubility or nilpotence.

Accordingly we have given some proofs in considerable detail, though of course it is in the nature of such areport that many proofs have to be omitted or can only be given in outline.

WEIL, together with their schools, established the methods of modern abstract algebraic geometry which, rejecting the c1assical restriction to the complex groundfield, gave up geometrical intuition and undertook arithmetisation under the growing influence of abstract algebra.

VI closely related to finite dimensional locally convex spaces than are normed spaces. Moreover, further classes of operators have been found which take the place of nuclear or absolutely summing operators in the theory of nuclear locally convex spaces.

The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo topic category (IV). It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV).

Our interest, by and large, is in a special class of discrete subgroups of Lie groups, viz., lattices (by a lattice in a locally compact group G, we mean a discrete subgroup H such that the homogeneous space GJ H carries a finite G-invariant measure). It is assumed that the reader has considerable familiarity with Lie groups and algebraic groups.

Our own tables (on pages 134-142) deal with groups of low order, finite and infinite groups of congruent transformations, symmetric and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions.