Clifford Theory for Glider Representations
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- 作者：Frederik Caenepeel ; Fred Van Oystaeyen
- 关键词：Clifford theory ; Fragment
- 刊名：Algebras and Representation Theory
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：19
- 期：6
- 页码：1477-1493
- 全文大小：525 KB
- 刊物主题：Commutative Rings and Algebras; Associative Rings and Algebras; Non-associative Rings and Algebras;
- 出版者：Springer Netherlands
- ISSN：1572-9079
- 卷排序：19
文摘
Classical Clifford theory studies the decomposition of simple G-modules into simple H-modules for some normal subgroup H ⊲ G. In this paper we deal with chains of normal subgroups 1⊲G1⊲· · ·⊲Gd = G, which allow to consider fragments and in particular glider representations. These are given by a descending chain of vector spaces over some field K and relate different representations of the groups appearing in the chain. Picking some normal subgroup H ⊲ G one obtains a normal subchain and one can construct an induced fragment structure. Moreover, a notion of irreducibility of fragments is introduced, which completes the list of ingredients to perform a Clifford theory.