INTERVAL GARSIDE STRUCTURES FOR THE COMPLEX BRAID GROUPS B(e, e, n)

Neaime G (2019)
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 372(12): 8815-8848.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We define geodesic normal forms for the general series of complex reflection groups G(e, e, n). This requires the elaboration of a combinatorial technique in order to explicitly determine minimal word representatives of the elements of G(e, e, n) over the generating set of the presentation of Corran-Picantin. Using these geodesic normal forms, we construct intervals in G(e, e, n) that are proven to be lattices. This gives rise to interval Garside groups. We determine which of these groups are isomorphic to the complex braid group B(e, e, n) and get a complete classification. For the other Garside groups that appear in our construction, we provide some of their properties and compute their second integral homology groups in order to understand these new structures.
Erscheinungsjahr
2019
Zeitschriftentitel
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Band
372
Ausgabe
12
Seite(n)
8815-8848
ISSN
0002-9947
eISSN
1088-6850
Page URI
https://pub.uni-bielefeld.de/record/2941904

Zitieren

Neaime G. INTERVAL GARSIDE STRUCTURES FOR THE COMPLEX BRAID GROUPS B(e, e, n). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 2019;372(12):8815-8848.
Neaime, G. (2019). INTERVAL GARSIDE STRUCTURES FOR THE COMPLEX BRAID GROUPS B(e, e, n). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 372(12), 8815-8848. doi:10.1090/tran/7885
Neaime, G. (2019). INTERVAL GARSIDE STRUCTURES FOR THE COMPLEX BRAID GROUPS B(e, e, n). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 372, 8815-8848.
Neaime, G., 2019. INTERVAL GARSIDE STRUCTURES FOR THE COMPLEX BRAID GROUPS B(e, e, n). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 372(12), p 8815-8848.
G. Neaime, “INTERVAL GARSIDE STRUCTURES FOR THE COMPLEX BRAID GROUPS B(e, e, n)”, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 372, 2019, pp. 8815-8848.
Neaime, G.: INTERVAL GARSIDE STRUCTURES FOR THE COMPLEX BRAID GROUPS B(e, e, n). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 372, 8815-8848 (2019).
Neaime, Georges. “INTERVAL GARSIDE STRUCTURES FOR THE COMPLEX BRAID GROUPS B(e, e, n)”. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 372.12 (2019): 8815-8848.

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