Two-step nilpotent Lie algebras

ABSTRACT ............................................ iv
INTRODUCTION .................. 1
THE DUALITY . . ...................................... 4
The Cohomology Ring of a Lie Algebra ............ 4
Definition and First Properties of N* . . . . . . B
The Involutive Property ........................ 12
The Main Result of Chapter I I .................. 15
THE INVARIANT ........................................ 17
The Function I .................................. 17
The Universal Enveloping Algebra . . . . . . . . . 19
The Main Result of Chapter I I I .................. 21
EXAMPLES ............................................. 25
The Case dim N = 6, dim N» = 2 .................. 25
The Hessian. . . . . . . . . . . . . . . . . . . . 29
Certain Algebras N with dim N = B, dim Nr = 2 . . 30
The Case Where (dim N - dim NT) is Odd . . . . . . 32
Certain Algebras N With dim N = 10, dim Nf = 5 . . 33
Certain Three-Step Nilpotent Lie Algebras . . . . 35
FURTHER RESULTS ...................................... 3#
{l(B)} is not a Complete Set of Invariants . . . . 3&
Extending the Definition of the Invariant . . . . 39
A Duality for Certain Almost-Algebraic Algebras . 42
CONCLUSIONS .......................................... 47
LIST OF REFERENCES ................................. 49
APPENDIX ............................................ 50
VITA 52