Examples of Solvable Lie Foliation

The Diffeomorphism Group of a Lie Foliation

We explicitly compute the diffeomorphism group of several types of linear foliations (with dense leaves) on the torus T, n ≥ 2, namely codimension one foliations, flows, and the so-called nonquadratic foliations. We show in particular that non-quadratic foliations are rigid, in the sense that they do not admit transverse diffeomorphisms other than ±id and translations. The computation is an app...

Classification of Solvable Lie Algebras

Several classifications of solvable Lie algebras of small dimension are known. Up to dimension 6 over a real field they were classified by G. M. Mubarakzjanov [Mubarakzjanov 63a, Mubarakzjanov 63b], and up to dimension 4 over any perfect field by J. Patera and H. Zassenhaus [Patera and Zassenhaus 90]. In this paper we explore the possibility of using the computer to obtain a classification of s...

Solvable Lie algebras with $N(R_n,m,r)$ nilradical

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.

On the Lie Algebra of a Transversally Complete Foliation

Examples of Homotopy Lie Algebras

We look at two examples of homotopy Lie algebras (also known as L∞ algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators ∆ to verify the homotopy Lie data is shown to produce the sa...