We show that the category A(G) of actions of a locally compact group G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma category of norm...

We prove that a maximal surface in Lorentz-Minkowski space L3 can be extended analytically along its boundary if the boundary lies in a plane meeting the surface at a constant angle.

Exercise 10.3.2. Let R be a commutative ring with identity. For all positive integers n and m, R ∼= R if and only if n = m. Proof. Let φ : R → R be an isomorphism of R-modules and let I E R be a maximal ideal. Then the map φ̄ : R → R/IR given by φ̄(α) = φ(α) is a morphism of R-modules. Moreover ker φ̄ = {α ∈ R | φ̄(α) = 0} = {α ∈ R | φ(α) ∈ IR} = φ−1(IRm) = IR. Therefore by the first isomorphism th...

A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite Heisenberg groups.

We prove that the operators in a class of rough fractional integral operators and the related maximal operators are bounded from L p (v p) to L q (u q) with weight pair (u,v).

We show that for hypergraphs of bounded edge size, the problem of extending a given list of maximal independent sets is NC-reducible to the computation of an arbitrary maximal independent set for an induced sub-hypergraph. The latter problem is known to be in RNC. In particular, our reduction yields an incremental RNC dualization algorithm for hypergraphs of bounded edge size, a problem previou...

The n-dimensional hypercube Qn has many maximal independent sets of vertices. We study the cardinality of those maximal independent sets which are balanced , i.e. exactly half of whose vertices have even weight, obtaining both upper and lower bounds for the maximum value. For n ≤ 7 we obtain the exact value. For all odd n, we conjecture that the exact value is 2n−1 − ( n−1 (n−1)/2 ) . We also c...

Let k be an algebraically closed field, G a connected reductive group over k, and A a maximal torus in G. We write g for the Lie algebra of G and a for X∗(A)⊗ZR. Let F = k((ǫ)) be the field of formal Laurent series over k and let o = k[[ǫ]] be the subring of formal power series. We fix an algebraic closure F̄ of F . We write G and g for G(F ) and g(F ) := g ⊗k F respectively. Let y ∈ a and write...

We survey some recent results on maximal subgroups of finite classical groups. WE MUST LIVE IN HOPE!!! (R.H. Dye, Newcastle Upon Tyne, Summer 1996)

Very little is known regarding the Galois group of the maximal p-extension unramified outside a finite set of primes S of a number field in the case that the primes above p are not in S. We describe methods to compute this group when it is finite and conjectural properties of it when it is infinite.