The Dynkin diagram cohomology of finite Coxeter groups
Let D be a connected graph. The Dynkin complex C D (A) of a D-algebra A was introduced by the second author to control the deformations of quasi-Coxeter algebra structures on A. In the present paper, we study the cohomology of this complex when A is the group algebra of a Coxeter group W and D is th...
| প্রধান লেখক: | , |
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| বিন্যাস: | Journal article |
| ভাষা: | English |
| প্রকাশিত: |
Elsevier
2010
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| সংক্ষিপ্ত: | Let D be a connected graph. The Dynkin complex C D (A) of a D-algebra A was introduced by the second author to control the deformations of quasi-Coxeter algebra structures on A. In the present paper, we study the cohomology of this complex when A is the group algebra of a Coxeter group W and D is the Dynkin diagram of W. We compute this cohomology when W is finite and prove in particular the rigidity of quasi-Coxeter algebra structures on kW. For an arbitrary W, we compute the top cohomology group and obtain a number of additional partial results when W is affine. Our computations are carried out by filtering the Dynkin complex by the number of vertices of subgraphs of D. The corresponding graded complex turns out to be dual to the sum of the Coxeter complexes of all standard, irreducible parabolic subgroups of W. © 2009 Elsevier Inc. All rights reserved. |
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