This book introduces a new class of non-associative algebras related to
certain exceptional algebraic groups and their associated buildings.
Richard Weiss develops a theory of these "quadrangular algebras" that
opens the first purely algebraic approach to the exceptional Moufang
quadrangles. These quadrangles include both those that arise as the
spherical buildings associated to groups of type E6, E7, and E8 as well
as the exotic quadrangles "of type F4" discovered earlier by Weiss.
Based on their relationship to exceptional algebraic groups,
quadrangular algebras belong in a series together with alternative and
Jordan division algebras. Formally, the notion of a quadrangular algebra
is derived from the notion of a pseudo-quadratic space (introduced by
Jacques Tits in the study of classical groups) over a quaternion
division ring. This book contains the complete classification of
quadrangular algebras starting from first principles. It also shows how
this classification can be made to yield the classification of
exceptional Moufang quadrangles as a consequence. The book closes with a
chapter on isotopes and the structure group of a quadrangular algebra.
Quadrangular Algebras is intended for graduate students of mathematics
as well as specialists in buildings, exceptional algebraic groups, and
related algebraic structures including Jordan algebras and the algebraic
theory of quadratic forms.
