Quantum homogeneous spaces of connected Hopf algebras

Let H be a connected Hopf k-algebra of finite Gel'fand-Kirillov dimension over an algebraically closed field k of characteristic 0. The objects of study in this paper are the left or right coideal subalgebras T of H. They are shown to be deformations of commutative polynomial k-algebras. A number of well-known homological and other properties follow immediately from this fact. Further properties are described, examples are considered, invariants are constructed and a number of open questions are listed.Comment: 26 pages; comments welcom

Supporting community engagement through teaching, student projects and research

The Education Acts statutory obligations for ITPs are not supported by the Crown funding model. Part of the statutory role of an ITP is “... promotes community learning and by research, particularly applied and technological research ...” [The education act 1989]. In relation to this a 2017 TEC report highlighted impaired business models and an excessive administrative burden as restrictive and impeding success. Further restrictions are seen when considering ITPs attract < 3 % of the available TEC funding for research, and ~ 20 % available TEC funding for teaching, despite having overall student efts of ~ 26 % nationally. An attempt to improve performance and engage through collaboration (community, industry, tertiary) at our institution is proving successful. The cross-disciplinary approach provides students high level experience and the technical stretch needed to be successful engineers, technologists and technicians. This study presents one of the methods we use to collaborate externally through teaching, student projects and research

Hopf algebras under finiteness conditions

This is a brief survey of some recent developments in the study of infinite dimensional Hopf algebras which are either noetherian or have finite Gelfand-Kirillov dimension. A number of open questions are listed.Comment: Comments welcom

The Biggest Auction Ever: the Sale of the British 3G Telecom Licenses

This paper reviews the part played by economists in organizing the British third-generation mobile-phone licence auction that concluded on 27 April 2000. It raised £22 1/2 billion ($34 billion or 2 1/2% of GNP) and was widely described at the time as the biggest auction ever. We discuss the merits of auctions versus "beauty contests", the aims of the auction, the problems we faced, the auction designs we considered, and the mistakes that were made.Auctions, Telecommunications, Spectrum Auctions, Mobile Phones, 3G, UMTS, Bidding.

A double-edged sword: Use of computer algebra systems in first-year Engineering Mathematics and Mechanics courses

Many secondary-level mathematics students have experience with graphical calculators from high school. For the purposes of this paper we define graphical calculators as those able to perform rudimentary symbolic manipulation and solve complicated equations requiring very modest user knowledge. The use of more advanced computer algebra systems e.g. Maple, Mathematica, Mathcad, Matlab/MuPad is becoming more prevalent in tertiary-level courses. This paper explores our students’ experience using one such system (MuPad) in first-year tertiary Engineering Mathematics and Mechanics courses. The effectiveness of graphical calculators and computer algebra systems in mathematical pedagogy has been investigated by a multitude of educational researchers (e.g. Ravaglia et al. 1998). Most of these studies found very small or no correlation between student use of graphical calculators or exposure to computer algebra systems with future achievement in mathematics courses (Buteau et al. 2010). In this paper we focus instead on students’ attitude towards a more advanced standalone computer algebra system (MuPad), and whether students’ inclination to use the system is indicative of their mathematical understanding. Paper describing some preliminary research into use of computer algebra systems for teaching engineering mathematics

The R2 Puzzle

Previous research has argued that the degree of co-movement of stock returns (the R² of a market regression) at country-level can be explained by the interaction of firmspecific and market-wide information. The R² measure has been used to investigate a number of issues of potentially great importance to accounting, such as whether countries with poor corporate governance regimes and weak legal protection of private property rights are more likely to have poor information environments or to assess the informativeness of prices. To date, only limited research has been carried out to assess the reliability of an information interpretation of the R² measure at a firm-level within a country rather than at an aggregate country level. In this paper we now examine the properties of stock returns co-movement at the firm-level within two countries, UK and USA, thereby being able to filter out certain extraneous factors that could arise in cross-country settings. We analyse the performance of this overall measure by triangulating it with other information-related measures which previous research has suggested capture partial aspects of the information environment. We find some serious flaws in the methodology and our findings suggest that when using it at firm-level, it may be being driven by other factors related to uninformed trading.Information; R²; firm-specific information; market-wide information; volatility; disclosures; comovement