Publication Date

2009-04-25

Availability

Open access

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PHD)

Department

Mathematics (Arts and Sciences)

Date of Defense

2009-04-13

First Committee Member

Shulim Kaliman - Committee Chair

Second Committee Member

Bruno De Oliveira - Committee Member

Third Committee Member

Alexander Dvorsky - Committee Member

Fourth Committee Member

Orlando Alvarez - Outside Committee Member

Abstract

Let X be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that X is equipped with several fixed point free non-degenerate SL_2-actions satisfying some mild additional assumption. Then we prove that the Lie algebra generated by completely integrable algebraic vector fields on X coincides with the set of all algebraic vector fields. In particular, we show that apart from a few exceptions this fact is true for any homogeneous space of form G/R where G is a linear algebraic group and R is a proper reductive subgroup of G.

Keywords

Luna's Slice Theorem; Compatibility Condition

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