Supermanifolds and Supergroups Basic Theory [Paperback]

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.

- Preface. - I: U-graded commutative linear algebra. 1. U-graded commutative rings and U-graded A-modules. 2. (Multi-) linear maps. 3. Direct sums, free U-graded A-modules, and quotients. 4. Tensor products. 5. Exterior powers. 6. Algebras and derivations. 7. Identifications. 8. Isomorphisms. - II: Linear algebra of free graded A-modules. 1. Our kind of Z2-graded algebra A. 2. Free graded A-modules. 3. Constructions of free graded A-modules. 4. Linear maps and matrices. 5. The graded trace and the graded determinant. 6. The body of a free graded A-modulÓ>