Search

For any closed oriented manifold $M$, the top degree multi-vector fields transverse to the zero section of $\wedge^{{\rm top}}TM$ are classified, up to orientation preserving diffeomorphism, in terms of the topology of the arrangement of their zero locus and a finite number of numerical invariants. The group governing the infinitesimal deformations of such multi-vector fields is computed, and an explicit set of generators exhibited. For the sphere $S^n$, a correspondence between certain isotopy classes of multi-vector fields and classes of weighted signed trees is established.

We prove Pursell–Shanks type results for the Lie algebra $\mathcal{D}(M)$ of all linear differential operators of a smooth manifold M, for its Lie subalgebra $\mathcal{D}^1(M)$ of all linear first-order differential operators of M and for the Poisson algebra S(M) = Pol(T*M) of all polynomial functions on T*M, the symbols of the operators in $\mathcal{D}(M)$. Chiefly, however, we provide explicit formulas completely describing the automorphisms of the Lie algebras $\mathcal{D}^1(M)$, S(M) and $\mathcal{D}(M)$.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

GLOBAL CLASSIFICATION OF GENERIC MULTI-VECTOR FIELDS OF TOP DEGREE

Automorphisms of quantum and classical Poisson algebras

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

GLOBAL CLASSIFICATION OF GENERIC MULTI-VECTOR FIELDS OF TOP DEGREE

Automorphisms of quantum and classical Poisson algebras