Bases for the derivation modules of two-dimensional ~multi-Coxeter arrangements and universal derivations
| Autor: | Atsushi Wakamiko |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
32S22 20F55
multi-arrangement General Mathematics Coxeter group Basis (universal algebra) Point group Coxeter arrangement primitive derivation Combinatorics logarithmic differential form Coxeter complex FOS: Mathematics multi-derivation module Mathematics - Combinatorics Artin group Combinatorics (math.CO) Orbit (control theory) Longest element of a Coxeter group Mathematics::Representation Theory Coxeter element 32S22 Mathematics |
| Zdroj: | Hokkaido Math. J. 40, no. 3 (2011), 375-392 |
| ISSN: | 0385-4035 |
| DOI: | 10.14492/hokmj/1319595862 |
| Popis: | Let $\A$ be an irreducible Coxeter arrangement and $\bfk$ be a multiplicity of $\A$. We study the derivation module $D(\A, \bfk)$. Any two-dimensional irreducible Coxeter arrangement with even number of lines is decomposed into two orbits under the action of the Coxeter group. In this paper, we will {explicitly} construct a basis for $D(\A, \bfk)$ assuming $\bfk$ is constant on each orbit. Consequently we will determine the exponents of $(\A, \bfk)$ under this assumption. For this purpose we develop a theory of universal derivations and introduce a map to deal with our exceptional cases. |
| Databáze: | OpenAIRE |
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