Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions

Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that the invariant ring $U^G$ is also polynomial. This contrasts with the case of \emph{linear and graded} group actions with polynomial rings of invariants, where the classical theorem of Chevalley-Shephard-Todd and Serre requires $G$ to be generated by pseudo-reflections. Our result is part of a general theory of "trace surjective $G$-algebras", which, in the case of $p$-groups, coincide with the Galois ring-extensions in the sense of \cite{chr}. We consider the \emph{dehomogenized symmetric algebra} $D_k$, a polynomial ring with non-linear $G$-action, containing $U$ as a retract and we show that $D_k^G$ is a polynomial ring. Thus $U$ turns out to be \emph{universal} in the sense that every trace surjective $G$-algebra can be constructed from $U$ by "forming quotients and extending invariants". As a consequence we obtain a general structure theorem for Galois-extensions with given $p$-group as Galois group and any prescribed commutative $k$-algebra $R$ as invariant ring. This is a generalization of the Artin-Schreier-Witt theory of modular Galois field extensions of degree $p^s$.Comment: 20 page

The Invariant Fields of the Sylow groups of Classical Groups in the natural characteristic

Let X be any finite classical group defined over a finite field of characteristic p>0. In this paper we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.Comment: 33 page

Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst

We consider the behaviour of a continuous super-Brownian motion catalysed by a random medium with infinite overall density under the hydrodynamic scaling of mass, time, and space. We show that, in supercritical dimensions, the scaled process converges to a macroscopic heat flow, and the appropriately rescaled random fluctuations around this macroscopic flow are asymptotically bounded, in the sense of log-Laplace transforms, by generalised stable Ornstein-Uhlenbeck processes. The most interesting new effect we observe is the occurrence of an index-jump from a 'Gaussian' situation to stable fluctuations of index 1+gamma, where gamma is an index associated to the medium.Comment: 40 page

The invariant fields of the Sylow groups of classical groups in the natural characteristic

Let X be any finite classical group defined over a finite field of characteristic p > 0. In this article, we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular, we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.info:eu-repo/semantics/publishedVersio

Acceptance of Speech-to-Text Technology: Exploring Language Proficiency and Psychological Safety in Global Virtual Teams

Natural Language Processing, such as speech-to-text technology, is increasingly implemented in collaboration software that is used by global virtual teams (GVT). GVT collaboration has become ubiquitous and has additionally accelerated during the COVID-19 pandemic. The main issues of global virtual teams are technology difficulties, language and time zone differences, and lower levels of psychological safety. Advances in collaboration technology aim at improving collaboration for GVT. But we know little about the acceptance of these technologies. Therefore, the objective of this study is to explore how Millennial and Gen Z members of GVT accept speech-to-text technology; namely, automated captions in virtual conferences and automated meetings transcripts. Particularly, we are comparing antecedents of acceptance across levels of language proficiency and psychological safety. We surveyed 530 users of speech-to-text technology in GVT both before and after they used the technology. The pre-survey was administered before the COVID-19 pandemic hit; when participants completed the post-survey all were under some degree of lockdown. Results suggest that use of the technology reduces anxiety and effort, but decreases performance expectation and hedonic motivation. Non-native speakers rate the technology more positively. The impact of psychological safety is limited to self-efficacy and anxiety

The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic

Let G be a Sylow p-subgroup of the unitary groups GU(3, q2), GU(4, q2), the symplectic group Sp(4, q) and, for q odd, the orthogonal group O +(4, q). In this paper we construct a presenta tion for the invariant ring of G acting on the natural module. In particular we prove that these rings are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant form defining the corresponding classical group. We also show that these generators form a SAGBI basis and the invariant ring for G is a complete intersection.info:eu-repo/semantics/publishedVersio

Smart Collaboration in Global Virtual Teams: The Influence of Culture on Technology Acceptance and Communication Effectiveness

Teams are beginning to rely on smart communication technology that is enhanced by Artificial Intelligence (AI). Yet, we lack understanding of how these smart communication technologies (SCT) influence team collaboration, especially in global virtual teams (GVT). This study empirically investigates how cultural values and practices influence the acceptance of SCT and how the use of this technology impacts communication effectiveness in GVT. We surveyed 643 members of 109 GVT before and after using the SCT. Results showed that team members from individualistic, future oriented cultures generally had more positive expectations towards the performance and enjoyment of using the technology. Uncertainty avoidance increased effort expectancy. After using SCT for communicating in the GVT, most differences disappeared. Regarding communication effectiveness, SCT had a positive influence, which was stronger for performance and future oriented cultures

Language Proficiency and Media Synchronicity Theory: The Impact of Media Capabilities on Satisfaction and Inclusion in Multilingual Virtual Teams

Virtual teams that use integrated communication technologies are ubiquitous in cross-border collaboration. This study explored media use and communication performance in multilingual virtual teams. Based on surveys from 96 virtual teams (with 578 team members), the research showed that more time spent in synchronous communication channels such as online conferences increased inclusion and satisfaction. Team members with lower language proficiency felt less included in synchronous and asynchronous collaboration, whereas team members with higher language proficiency felt less satisfied with asynchronous collaboration. Also, limited language proficiency speakers were significantly less likely to view synchronous tools as helpful for their teams to reach a mutual decision. Our data supports Media Synchronicity Theory (MST) for native and highly proficient English speakers. However, MST needs to be adjusted to account for different levels of language proficiency

Aerobic biodegradation of chiral phenoxyalkanoic acid derivatives during incubations with activated sludge

The aerobic biodegradation of racemic mixtures of five chiral phenoxyalkanoic acids was studied according to a biodegradation test that was complemented with enantiomer-specific analysis. Both enantiomers of (RS)-2-phenoxypropanoic acid, (RS)-2-(3-chlorophenoxy)propanoic acid, and (RS)-2-(4-chlorophenoxy)propanoic acid, were completely degraded within 25 days when aerobically incubated with activated sludge. During incubations of (RS)-2-phenoxypropanoic acid, the (R) enantiomer was degraded before the (S) enantiomer, whereas during incubations of (RS)-2-(3-chlorophenoxy)propanoic acid the (S) enantiomer was preferentially degraded. The (R) enantiomer of (RS)-2-(2-chlorophenoxy)propanoic acid was removed after 24 days while only 30% of the (S) enantiomer was degraded within 47 days of incubation. (RS)-2-(2,4,5-Trichlorophenoxy)propanoic acid was the most persistent of all the racemic mixtures tested. After 47 days, the concentration of the (S) enantiomer was nearly unchanged, and the concentration of (R)-2-(2,4,5-trichlorophenoxy)propanoic acid had decreased only by about 40%. The differences observed in the length of the lag phases and in the degradation rates of individual enantiomers can lead to accumulations of the more recalcitrant enantiomer in aquatic or terrestrial ecosystem

Recorded Work Meetings and Algorithmic Tools: Anticipated Boundary Turbulence

Meeting recordings and algorithmic tools that process and evaluate recorded meeting data may provide many new opportunities for employees, teams, and organizations. Yet, the use of this data raises important consent, data use, and privacy issues. The purpose of this research is to identify key tensions that should be addressed in organizational policymaking about data use from recorded work meetings. Based on interviews with 50 professionals in the United States, China, and Germany, we identify the following five key tensions (anticipated boundary turbulence) that should be addressed in a social contract approach to organizational policymaking for data use of recorded work meetings: disruption versus help in relationships, privacy versus transparency, employee control versus management control, learning versus evaluation, and trust in AI versus trust in people