Universal deformation rings and dihedral 2-groups

Let $k$ be an algebraically closed field of characteristic 2, and let $W$ be the ring of infinite Witt vectors over $k$. Suppose $D$ is a dihedral 2-group. We prove that the universal deformation ring $R(D,V)$ of an endo-trivial $kD$-module $V$ is always isomorphic to $W[\mathbb{Z}/2\times\mathbb{Z}/2]$. As a consequence we obtain a similar result for modules $V$ with stable endomorphism ring $k$ belonging to an arbitrary nilpotent block with defect group $D$. This confirms for such $V$ conjectures on the ring structure of the universal deformation ring of $V$ which had previously been shown for $V$ belonging to cyclic blocks or to blocks with Klein four defect groups.Comment: 16 pages, 1 tabl

Large universal deformation rings

We provide a series of examples of finite groups G and mod p representations V of G whose stable endomorphisms are all given by scalars such that V has a universal deformation ring R(G,V) which is large in the sense that R(G,V)/pR(G,V) is isomorphic to a power series algebra in one variable.Comment: 9 pages, 5 figures; for Prop. 2, the description of the groups and the proof have slightly change

Dihedral blocks with two simple modules

Let $k$ be an algebraically closed field of characteristic 2, and let $G$ be a finite group. Suppose $B$ is a block of $kG$ with dihedral defect groups such that there are precisely two isomorphism classes of simple $B$-modules. The description by Erdmann of the quiver and relations of the basic algebra of $B$ is usually only given up to a certain parameter $c$ which is either 0 or 1. In this article, we show that $c=0$ if there exists a central extension $\hat{G}$ of $G$ by a group of order 2 together with a block $\hat{B}$ of $k\hat{G}$ with generalized quaternion defect groups such that $B$ is contained in the image of $\hat{B}$ under the natural surjection from $k\hat{G}$ onto $kG$. As a special case, we obtain that $c=0$ if $G=\mathrm{PGL}_2(\mathbb{F}_q)$ for some odd prime power $q$ and $B$ is the principal block of $k \mathrm{PGL}_2(\mathbb{F}_q)$.Comment: 11 pages, 5 figures. The arguments work also for non-principal blocks. The paper has been changed accordingly; in particular, the word "principal" was removed from the titl

Universal deformation rings and dihedral defect groups

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group, and B is a block of kG with dihedral defect group D which is Morita equivalent to the principal 2-modular block of a finite simple group. We determine the universal deformation ring R(G,V) for every kG-module V which belongs to B and has stable endomorphism ring k. It follows that R(G,V) is always isomorphic to a subquotient ring of WD. Moreover, we obtain an infinite series of examples of universal deformation rings which are not complete intersections.Comment: 37 pages, 13 figures. Changed introduction, updated reference

OLong-run Money Demand in OECD Countries – Cross-Member Cointegration

This paper examines the long-run money demand function for 11 OECD countries from 1983 to 2006 using panel data and including wealth. The distinction between common factors and idiosyncratic components using principal component analysis allows to detect cross-member cointegration and to distinguish between international and national developments as drivers of the long-run relation between money and its determinants. Indeed, cointegration between the common factors of the underlying variables, i.e. cross-member cointegration, indicates that the long-run relationship is mainly driven by international stochastic trends. Furthermore, it is found that the impact of income on money demand is positive, while it is negative for the interest rate and stock prices. The estimated (semi-)elasticities of money are larger for the common factors than for the original variables, except the income elasticity. Finally, the results of a panel-based error-correction model suggest that money demand converges to an international cross-member equilibrium relation of the common factors.Money demand; wealth effects; panel unit roots; vector error-correction models

Euro area private consumption: Is there a role for housing wealth effects

This paper adds to the literature on wealth effects on consumption by disentangling financial wealth effects from housing wealth effects for the euro area. We use two macro-datasets for our estimations, one on the aggregate euro area for the period 1980-2006, and one on the individual euro area countries from1995-2006, using panel data techniques. The impact of all wealth variables on euro area consumption is significant and positive in most specifications for both datasets. The marginal propensity to consume (MPC) out of financial wealth is roughly in line with the literature, with 2.4 to 3.6 cents per euro of financial wealth spent on consumption according to the estimations with euro area aggregate data. However, the panel estimation yields somewhat lower results (0.6 to 1.1 cents). The MPC out of nominal housing wealth lies between 0.7 to 0.9 cents per euro for both datasets. When specifying housing wealth in real terms, i.e. when taking out the effect of volatile house prices, we find similar effects in the times series estimation while the MPC is larger in the panel estimation (2.5 cents). JEL Classification: E21Consumption, euro area, financial wealth, housing wealth

Survey Methodology: International Developments

Falling response rates and the advancement of technology have shaped the discussion in survey methodology in the last few years. Both led to a notable change in data collection efforts. Survey organizations try to create adaptive recruitment and survey designs and increased the collection of non-survey data for sampled cases. While the first strategy is an attempt to increase response rates and to save cost, the latter is part of efforts to reduce possible bias and response burden of those interviewed. To successfully implement adaptive designs and alternative data collection efforts researchers need to understand error properties of mixedmode and multiple-frame surveys. Randomized experiments might be needed to gain that knowledge. In addition close collaboration between survey organizations and researchers is needed, including the possibility and willingness to shared data between those organizations. Expanding options for graduate and post-graduate education in survey methodology might help to increase the possibility for high quality surveys.Survey Methodology, Responsive Design, Paradata