Supermanifolds and Supergroups

Basic Theory
2004. Auflage 2004
ISBN: 978-1-4020-2296-8
Verlag: Springer

Buch, Englisch, 416 Seiten, Format (B × H): 169 mm x 249 mm, Gewicht: 1720 g

Reihe: Mathematics and Its Applications

Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections.

The book requires standard undergraduate knowledge on super differential geometry and super Lie groups.

Zielgruppe

Research

Autoren/Hrsg.

Tuynman, Gijs M

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

$$ \mathfrak{A} $$ -graded commutative linear algebra.- Linear algebra of free graded A-modules.- Smooth functions and A-manifolds.- Bundles.- The tangent space.- A-Lie groups.- Connections.