Glider Representations of Group Algebra Filtrations of Nilpotent Groups

Glider Representations of Group Algebra Filtrations of Nilpotent Groups We continue the study of glider representations of finite groups G with given structure chain of subgroups e ⊂ G 1 ⊂… ⊂ G d = G. We give a characterization of irreducible gliders of essential length e ≤ d which in the case of p-groups allows to prove some results about classical representation theory. The paper also contains an introduction to generalized character theory for glider representations and an extension of the decomposition groups in the Clifford theory. Furthermore, we study irreducible glider representations for products of groups and nilpotent groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebras and Representation Theory Springer Journals

Glider Representations of Group Algebra Filtrations of Nilpotent Groups

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Mathematics; Commutative Rings and Algebras; Associative Rings and Algebras; Non-associative Rings and Algebras
ISSN
1386-923X
eISSN
1572-9079
D.O.I.
10.1007/s10468-017-9725-9
Publisher site
See Article on Publisher Site

Abstract

We continue the study of glider representations of finite groups G with given structure chain of subgroups e ⊂ G 1 ⊂… ⊂ G d = G. We give a characterization of irreducible gliders of essential length e ≤ d which in the case of p-groups allows to prove some results about classical representation theory. The paper also contains an introduction to generalized character theory for glider representations and an extension of the decomposition groups in the Clifford theory. Furthermore, we study irreducible glider representations for products of groups and nilpotent groups.

Journal

Algebras and Representation TheorySpringer Journals

Published: Jul 31, 2017

References

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