Inductive Algebras for Finite Heisenberg Groups
نویسندگان
چکیده
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.
منابع مشابه
Vertex Representations via Finite Groups and the Mckay Correspondence
where the first factor is a symmetric algebra and the second one is a group algebra. The affine algebra ĝ contains a Heisenberg algebra ĥ. One can define the so-called vertex operators X(α, z) associated to α ∈ Q acting on V essentially using the Heisenberg algebra ĥ. The representation of ĝ on V is then obtained from the action of the Heisenberg algebra ĥ and the vertex operators X(α, z) assoc...
متن کاملClassification Theorems for Finite Group Actions Using the Equivariant Cuntz Semigroup
We classify actions of finite groups on some class of C*-algebras with the Rokhlin property in terms of the Cuntz semigroup. An obstruction is obtained for the Cuntz semigroup of a C*-algebra allowing such an action. We also classify certain inductive limit actions of finite groups on a class of C*-algebras containing AI-algebras. This classification is done via the equivariant Cuntz semigroup.
متن کاملSmarandache algebras and their subgroups
In this paper we define S algebras and show that every finite group can be found in some S algebra. We define and study the S degree of a finite group and determine the S degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $D_p$.
متن کاملCharacterization of Simple Highest Weight Modules
We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro and for Heisenberg algebras.
متن کاملBlaschke Inductive Limits of Uniform Algebras
We consider and study Blaschke inductive limit algebras A(b), defined as inductive limits of disc algebras A(D) linked by a sequence b = {Bk}k=1 of finite Blaschke products. It is well known that big G-disc algebras AG over compact abelian groups G with ordered duals Γ = Ĝ ⊂Q can be expressed as Blaschke inductive limit algebras. Any Blaschke inductive limit algebraA(b) is a maximal and Dirichl...
متن کامل