Quasi-homomorphism rigidity with non-commutative targets

Non Commutative Chern - Weil Homomorphism

Towards the Chern-weil Homomorphism in Non Commutative Differential Geometry

In this short review article we sketch some developments which should ultimately lead to the analogy of the Chern-Weil homomorphism for principle bundles in the realm of non commutative differential geometry. Principal bundles there should have Hopf algebras as structure ‘cogroups’. Since the usual machinery of Lie algebras, connection forms, etc., just is not available in this setting, we base...

On quasi-zero divisor graphs of non-commutative rings

Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...

A Structured Multisignature based on a Non-Commutative Ring Homomorphism

Users’ signing order is an important factor in multisignature schemes. In fact the signing order often reflects signer’s rank in a signing group. So far, many multisignature schemes, called structured schemes, have been proposed that provide verifiability of the signing order associated with the structure of a group of signers. However, there are not many structured multisignature schemes utili...

Quasi-Particles in Non-Commutative Field Theory

After a short introduction to the UV/IR mixing in non-commutative field theories we review the properties of scalar quasi-particles in noncommutative supersymmetric gauge theories at finite temperature. In particular we discuss the appearance of super-luminous wave propagation. 1 Talk given at NATO ARW ”Non-Commutative Structures in Mathematics and Physics”, Kyiv 24-27 Sep. 2000