A Swan-like theorem

A Swan-like theorem

For purposes of implementing field arithmetic in F2n efficiently, it is desirable to have an irreducible polynomial f(x) ∈ F2[x] of degree n with as few terms as possible. The number of terms must be odd, as otherwise x+1 would be a factor. Often a trinomial x+x+1 can be found, or at least a pentanomial, x+x1 +x2 +x3 +1, where n > m1 > m2 > m3 > 0. If α is a root of f , then {1, α, α, . . . , α...

Serre-Swan theorem for non-commutative C∗-algebras. Revised edition

We generalize the Serre-Swan theorem to non-commutative C∗algebras. For a Hilbert C∗-module X over a C∗-algebra A, we introduce a hermitian vector bundle EX associated to X . We show that there is a linear subspace ΓX of the space of all holomorphic sections of EX and a flat connection D on EX with the following properties: (i) ΓX is a Hilbert A-module with the action of A defined by D, (ii) th...

Serre-Swan Theorem for non commutative C∗-algebras

A Serre-swan Theorem for Gerbe Modules on Étale Lie Groupoids

Given a torsion bundle gerbe on a compact smooth manifold or, more generally, on a compact étale Lie groupoid M , we show that the corresponding category of gerbe modules is equivalent to the category of finitely generated projective modules over an Azumaya algebra on M . This result can be seen as an equivariant Serre-Swan theorem for twisted vector bundles.

The Journal: A Swan-Song