Axioms, Volume 1, Issue 2

Since the advent of Drinfel’d’s double construction, Hopf algebraic structures have been a centrepiece for many developments in the theory and analysis of integrable quantum systems. An integrable anyonic pairing Hamiltonian will be shown to admit Ho...

The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in question f...

Using the most elementary methods and considerations, the solution of the star-triangle condition (a2+b2-c2)/2ab = ((a’)^2+(b’)^2-(c’))^2/2a’b’ is shown to be a necessary condition for the extension of the operator coalgebra of the six-vertex model t...

We study the duality between corings and ring extensions. We construct a new category with a self-dual functor acting on it, which extends that duality. This construction can be seen as the non-commutative case of another duality extension: the duali...

In computer science the Myhill–Nerode Theorem states that a set L of words in a finite alphabet is accepted by a finite automaton if and only if the equivalence relation ∼L, defined as x ∼L y if and only if xz ∈ L exactly when yz ∈ L, ∀z, has finite...

Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of indeterminates): . It is shown that an associative algebra A with a Hasse-Schmidt derivation ) on it is exactly the same as an NSymm module algebra. The primitive...

We investigate the interplay between the existence of fat triangulations, P L approximations of Lipschitz–Killing curvatures and the existence of quasiconformal mappings. In particular we prove that if there exists a quasiconformal mapping between tw...

Quivers (directed graphs), species (a generalization of quivers) and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to t...