Chapter 1 Introduction ......................................... 1
Acknowledgements ................................................ 4
Chapter 2 Preliminaries ........................................ 5
2.1 Superalgebras, superspaces, supergroups .................... 5
2.2 Lie superalgebras .......................................... 9
2.3 Homogeneous one-parameter supersubgroups .................. 11
Chapter 3 Chevalley bases and Chevalley algebras .............. 15
3.1 Root systems .............................................. 15
3.2 Chevalley bases and algebras .............................. 17
3.3 Existence of Chevalley bases .............................. 18
Chapter 4 Kostant superalgebras ............................... 25
4.1 Kostant's  -form .......................................... 25
4.2 Commutation rules ......................................... 26
4.3 Kostant's PBW-like theorem ................................ 28
Chapter 5 Chevalley supergroups ............................... 33
5.1 Admissible lattices ....................................... 34
5.2 Construction of Chevalley supergroups ..................... 35
5.3 Chevalley supergroups as algebraic supergroups ............ 39
5.4 Independence of Chevalley and Kostant superalgebras ....... 47
5.5 Lie's Third Theorem for Chevalley supergroups ............. 48
Chapter 6 The cases A(1,1), P(3) and Q(n) ..................... 51
6.1 Chevalley bases and Chevalley superalgebras ............... 52
6.2 Kostant superalgebras ..................................... 55
6.3 Chevalley supergroups and their properties ................ 57
Appendix A Sheafification ..................................... 59
Bibliography ................................................... 63
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