Search results for "Presentation"

The Bohm-Aharonov effect: A seven-dimensional structural group

1996

We realize a nonfaithful representation of a seven-dimensional Lie algebra, the extension of which to its universal enveloping algebra contains most of the observables of the scattering Aharonov-Bohm effect, as essentially self-adjoint operators: the scattering Hamiltonian, the total and kinetic angular momenta, the positions and the kinetic momenta. By restriction, we obtain the model introduced in Lett. Math. Phys.1 (1976), 155–163.

The Representation Type of the Centre of a Group Algebra

1986

Performance Reporting – The IASB's Proposed Formats of Financial Statements in the Exposure Draft of IAS 1

2006

ABSTRACT This paper is a response to the exposure draft of proposed amendments to IAS 1 Presentation of Financial Statements published by the International Accounting Standards Board (IASB) in March 2006. The objective is to bring to the standard setter's attention research that is relevant to the issues raised in the exposure draft. We review analytic, empirical and experimental research that addresses the presentation of income and the format of the income statement. Overall, there is some support for a single statement of (total) recognised income and expense. However, net income is on average more relevant than comprehensive income, which may favour a two-statement approach. While this …

Financial doping and financial fair play in European Club football competitions

2018

This contribution provides an explanation of ‘financial doping’ as a management concept in the context of European club football as well as on UEFA’s Financial Fair Play (FFP) regime, which can well be framed as the governing body of European football’s attempt to address this issue. The chapter is structured as follows: First, the historic development of financial regulation in European football is briefly outlined. The notion of financial doping as well as in what way it undermines the integrity of the sporting competition is addressed next. Afterwards, the FFP policy is explained, followed by a critical review of its discussion in scholarly literature as well as the presentation of an ou…

The multiplex structure of interbank networks

2013

The interbank market has a natural multiplex network representation. We employ a unique database of supervisory reports of Italian banks to the Banca d'Italia that includes all bilateral exposures broken down by maturity and by the secured and unsecured nature of the contract. We find that layers have different topological properties and persistence over time. The presence of a link in a layer is not a good predictor of the presence of the same link in other layers. Maximum entropy models reveal different unexpected substructures, such as network motifs, in different layers. Using the total interbank network or focusing on a specific layer as representative of the other layers provides a po…

Groups with few $p'$-character degrees

2019

Abstract We prove a variation of Thompson's Theorem. Namely, if the first column of the character table of a finite group G contains only two distinct values not divisible by a given prime number p > 3 , then O p p ′ p p ′ ( G ) = 1 . This is done by using the classification of finite simple groups.

A characterisation of nilpotent blocks

2015

Let $B$ be a $p$-block of a finite group, and set $m=$ $\sum \chi(1)^2$, the sum taken over all height zero characters of $B$. Motivated by a result of M. Isaacs characterising $p$-nilpotent finite groups in terms of character degrees, we show that $B$ is nilpotent if and only if the exact power of $p$ dividing $m$ is equal to the $p$-part of $|G:P|^2|P:R|$, where $P$ is a defect group of $B$ and where $R$ is the focal subgroup of $P$ with respect to a fusion system $\CF$ of $B$ on $P$. The proof involves the hyperfocal subalgebra $D$ of a source algebra of $B$. We conjecture that all ordinary irreducible characters of $D$ have degree prime to $p$ if and only if the $\CF$-hyperfocal subgrou…

New Refinements of the McKay Conjecture for Arbitrary Finite Groups

2004

Let $G$ be an arbitrary finite group and fix a prime number $p$. The McKay conjecture asserts that $G$ and the normalizer in $G$ of a Sylow $p$-subgroup have equal numbers of irreducible characters with degrees not divisible by $p$. The Alperin-McKay conjecture is a version of this as applied to individual Brauer $p$-blocks of $G$. We offer evidence that perhaps much stronger forms of both of these conjectures are true.

Almost polynomial growth: Classifying varieties of graded algebras

2015

Let G be a finite group, V a variety of associative G-graded algebras and c (V), n = 1, 2, …, its sequence of graded codimensions. It was recently shown by Valenti that such a sequence is polynomially bounded if and only if V does not contain a finite list of G-graded algebras. The list consists of group algebras of groups of order a prime number, the infinite-dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with suitable gradings. Such algebras generate the only varieties of G-graded algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all sub…

On irreducible products of characters

2021

Abstract We study the problem when the product of two non-linear Galois conjugate characters of a finite group is irreducible. We also prove new results on irreducible tensor products of cross-characteristic Brauer characters of quasisimple groups of Lie type.