The algebraic structure of BRST operators and their applications
This book has three related but distinct parts. In §the first part of the book, we construct a new §sequence of generators of the BRST§complex and reformulate the BRST differential so §that it acts on elements of the complex much like §the Maurer-Cartan differential acts on left-§invariant forms. In particular, for an important §class of physical theories, we show that in fact the §differential is a Chevalley-Eilenberg differential. §In the second part of the book, we isolate a new §concept which we call the chain extension of a $D$-§algebra. We demonstrate that this idea is central to §to a number of applications to algebra and physics. §Chain extensions may be regarded as generalizations§of ordinary algebraic extensions of Lie algebras. §Applications of our §theory provide a new constructive approach to BRST §theories§which only contains three terms.§Finally, we show that a similar development provides §a method by which Lie algebra §deformations may be encoded into the structure maps §of an sh-Lie algebra with three terms.