Ebook: Supermanifolds and Supergroups: Basic Theory
Author: Gijs M. Tuynman (auth.)
- Tags: Differential Geometry, Topological Groups Lie Groups, Non-associative Rings and Algebras
- Series: Mathematics and Its Applications 570
- Year: 2005
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages i-xiii
$ mathfrak{A} $ -graded commutative linear algebra....Pages 1-54
Linear algebra of free graded A-modules....Pages 55-89
Smooth functions and A-manifolds....Pages 91-139
Bundles....Pages 141-201
The tangent space....Pages 203-263
A-Lie groups....Pages 265-334
Connections....Pages 335-404
Back Matter....Pages 405-416
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.
Content:
Front Matter....Pages i-xiii
$ mathfrak{A} $ -graded commutative linear algebra....Pages 1-54
Linear algebra of free graded A-modules....Pages 55-89
Smooth functions and A-manifolds....Pages 91-139
Bundles....Pages 141-201
The tangent space....Pages 203-263
A-Lie groups....Pages 265-334
Connections....Pages 335-404
Back Matter....Pages 405-416
....