2 Citations
UvA-DARE (Digital Academic Repository) On partition functions for 3-graphs
- Mathematics
- 2018
. A cyclic graph is a graph with at each vertex a cyclic order of the edges incident with it specified. We characterize which real-valued functions on the collection of cubic cyclic graphs are…
References
SHOWING 1-10 OF 18 REFERENCES
Algebra of 3-graphs
- Mathematics
- 2012
We introduce and study the structure of an algebra in the linear space spanned by all regular 3-valent graphs with a prescribed order of edges at every vertex, modulo certain relations. The role of…
Reflection positivity, rank connectivity, and homomorphism of graphs
- Mathematics
- 2004
It is shown that a graph parameter can be realized as the number of homomorphisms into a fixed (weighted) graph if and only if it satisfies two linear algebraic conditions: reflection positivity and…
Chern-Simons perturbation theory. II
- Physics
- 1994
We study the perturbation theory for three dimensional Chern--Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, the…
Symmetry, Representations, and Invariants
- Mathematics
- 2009
Lie Groups and Algebraic Groups.- Structure of Classical Groups.- Highest-Weight Theory.- Algebras and Representations.- Classical Invariant Theory.- Spinors.- Character Formulas.- Branching Laws.-…
Perturbative Aspects of the Chern-Simons Topological Quantum Field Theory
- Mathematics
- 1991
We investigate the Feynman-diagram perturbative expansion of the Chem-Simons topological quantum field theory. After introducing the theory, we compute the one-loop expectation value for knots and…
On the tensor system of a semisimple Lie algebra
- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1972
Abstract From the tensorial point of view, the essential characteristic of a semisimple lie algebra A is the non-singularity of the Killing form, since this enables one to construct a system of…
Graph Invariants Related to Statistical Mechanical Models: Examples and Problems
- MathematicsJ. Comb. Theory, Ser. B
- 1993
Abstract Spin models and vertex models on graphs are defined as appropriate generalizations of the Ising-Potts model of statistical mechanics. We review some of these state models and the graph…
Introduction to Vassiliev Knot Invariants
- Mathematics
- 2012
1. Knots and their relatives 2. Knot invariants 3. Finite type invariants 4. Chord diagrams 5. Jacobi diagrams 6. Lie algebra weight systems 7. Algebra of 3-graphs 8. The Kontsevich integral 9.…