Unitary units in modular group algebras
نویسنده
چکیده
Let p be a prime, K a field of characteristic p , G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g 7→ g of G extends linearly to KG ; this extension leaves V setwise invariant, and its restriction to V followed by v 7→ v gives an automorphism of V . The elements of V fixed by this automorphism are called unitary; they form a subgroup. Our first theorem describes the K and G for which this subgroup is normal in V . For each element g in G , let g denote the sum (in KG) of the distinct powers of g . The elements 1 + (g − 1)hg with g, h ∈ G are the bicyclic units of KG . Our second theorem describes the K and G for which all bicyclic units are unitary.
منابع مشابه
Association Schemes and Fusion Algebras (An Introduction)
We introduce the concept of fusion algebras at algebraic level, as a purely algebraic concept for the fusion algebras which appear in conformal field theory in mathematical physics. We first discuss the connection between fusion algebras at algebraic level and character algebras, a purely algebraic concept for Bose-Mesner algebras of association schemes. Through this correspondence, we establis...
متن کاملAlgebraic orbifold conformal field theories.
The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbif...
متن کاملReiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras
متن کامل
Periods and Special Values of L-functions
Introduction 1 1. Modular forms, congruences and the adjoint L-function 2 2. Quaternion algebras and the Jacquet-Langlands correspondence 6 3. Integral period relations for quaternion algebras over Q 8 4. The theta correspondence 12 5. Arithmetic of the Shimizu lift and Waldspurger’s formula 16 6. Hilbert modular forms, Shimura’s conjecture and a refined version 19 7. Unitary groups and Harris’...
متن کاملThe quantum dilogarithm and representations of quantized cluster varieties
To David Kazhdan for his 60th birthday " Loxadь sostoit iz trh neravnyh polovin ". 4 The quantum dilogarithm and its properties 26 4.1 The quantum logarithm function and its properties. . 1 " A horse consists of three unequal halves ". cf. A. de Barr, Horse doctor. Moscow 1868. Cluster varieties [FG2] are relatives of cluster algebras [FZI]. Cluster modular groups act by automor-phisms of clust...
متن کامل