Alternating Subalgebras of Hecke Algebras and Alternating Subgroups of Braid Groups

For a Coxeter system (G, S) the multi-parametric alternating subalgebra H + (G) of the Hecke algebra and the alternating subgroup ℬ + (G) of the braid group are defined. Two presentations for H + (G) and ℬ + (G) are given; one generalizes the Bourbaki presentation for the alternating subgroups of Co...

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Bibliographic Details
Published in:Communications in algebra 2014-05, Vol.42 (5), p.1921-1936
Main Authors: Ogievetsky, O. V., d'Andecy, L. Poulain
Format: Article
Language:English
Subjects:
Algebra
Alternating subalgebras
Alternating subgroups
Braid groups
Braiding
Coxeter graph
Coxeter groups
Generators
Graphs
Hecke algebras
Mathematics
Quantum Algebra
Subgroups
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Summary:For a Coxeter system (G, S) the multi-parametric alternating subalgebra H + (G) of the Hecke algebra and the alternating subgroup ℬ + (G) of the braid group are defined. Two presentations for H + (G) and ℬ + (G) are given; one generalizes the Bourbaki presentation for the alternating subgroups of Coxeter groups, another one uses generators related to edges of the Coxeter graph.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2012.751111