Book Review: Abstract analytic function theory and Hardy algebras

Classification Theory for Hardy Classes of Analytic Functions

Representation Theory of Analytic Holonomy C Algebras

Integral calculus on the space A/G of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well–suited for quantization of diffeomorphism invariant theories of connections. The general setting is provided by the abelian C–algebra of functions on A/G generated by Wilson loops (i.e., by the traces of holonomies of conn...

NLRCS International Congress Abstract Book

Lie Algebras: Abstract Theory of Weights

Proof. I will check the four axioms of the root system. (R1) Since |Φ∨| = |Φ|, then Φ∨ is finite. Since Φ spans E and α∨ is a non-zero scalar multiple of α for all α ∈ Φ, then Φ∨ spans E and 0 / ∈ Φ∨. (R2) Since (−α)∨ = 2(−α) ((−α),(−α)) = − 2α (α,α) = −α∨, then the only multiples of α∨ are ±α∨. (R3) I need to show that if α∨ ∈ Φ∨ then the reflection σα∨ leaves Φ∨ invariant. Let α in Φ, then fo...

Generalizing Computability Theory to Abstract Algebras

We present a survey of our work over the last few decades on generalizations of computability theory to many-sorted algebras. The following topics are discussed, among others: (1) abstract v concrete models of computation for such algebras; (2) computability and continuity, and the use of many-sorted topological partial algebras, containing the reals; (3) comparisons between various equivalent ...