Article

# Inductive Algebras for Finite Heisenberg Groups

03/2008; DOI:doi:10.1080/00927870902828520
Source: arXiv

ABSTRACT A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite Heisenberg groups. Comment: 5 pages

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##### Article:Submodule categories of wild representation type
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ABSTRACT: Let Λ be a commutative local uniserial ring with radical factor field k. We consider the category S(Λ) of embeddings of all possible submodules of finitely generated Λ-modules. In case Λ=Z/〈pn〉, where p is a prime, the problem of classifying the objects in S(Λ), up to isomorphism, has been posed by Garrett Birkhoff in 1934. In this paper we assume that Λ has Loewy length at least seven. We show that S(Λ) is controlled k-wild with a single control object I∈S(Λ). It follows that each finite dimensional k-algebra can be realized as a quotient End(X)/End(X)I of the endomorphism ring of some object X∈S(Λ) modulo the ideal End(X)I of all maps which factor through a finite direct sum of copies of I.
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##### Article:Even automorphisms of trees and inductive algebras
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ABSTRACT: Let (π, H) be a unitary representation of a locally compact group G. A commutative subalgebra A of B(H) is called π– inductive when π(g)Aπ(g −1) = A for all g. The classification of maximal inductive algebras sheds light on the possible realizations of π on function spaces. In this paper we deal with the automorphism group of a locally finite homogeneous tree and its principal series spherical representations. We show that for some exceptional representations there exists just one inductive algebra besides those known. Fi-nally, we generalize the main results to the subgroup of even automorphisms of the tree.
International Journal of Pure and Applied Mathematics ————————————————————————– Volume. 01/2006; 29:521-551.
• Subgroups of abelian groups. Garrett . 1934. Proc. Lond. Math. Soc 38 385-400.

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### Keywords

5 pages

classification result

finite Heisenberg group

finite Heisenberg groups

maximal abelian sub-algebras

normalized