Higher dimensional Automorphic Lie Algebras

The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key feature of the classification is the study of the algebras in the context of classical invariant theory. This provides on one hand a powerful tool from the computational point of view, on the other it opens new questions from an algebraic perspective, which suggest further applications of these algebras, beyond the context of integrable systems. In particular, the research shows that Automorphic Lie Algebras associated to the $\mathbb{T}\mathbb{O}\mathbb{Y}$ groups (tetrahedral, octahedral and icosahedral groups) depend on the group through the automorphic functions only, thus they are group independent as Lie algebras. This can be established by defining a Chevalley normal form for these algebras, generalising this classical notion to the case of Lie algebras over a polynomial ring.Comment: 43 pages, standard LaTeX2

Automorphic Lie Algebras and Cohomology of Root Systems

A cohomology theory of root systems emerges naturally in the context of Automorphic Lie Algebras, where it helps formulating some structure theory questions. In particular, one can find concrete models for an Automorphic Lie Algebra by integrating cocycles. In this paper we define this cohomology and show its connection with the theory of Automorphic Lie Algebras. Furthermore, we discuss its properties: we define the cup product, we show that it can be restricted to symmetric forms, that it is equivariant with respect to the automorphism group of the root system, and finally we show acyclicity at dimension two of the symmetric part, which is exactly what is needed to find concrete models for Automorphic Lie Algebras. Furthermore, we show how the cohomology of root systems finds application beyond the theory of Automorphic Lie Algebras by applying it to the theory of contractions and filtrations of Lie algebras. In particular, we show that contractions associated to Cartan $\mathbb{Z}$-filtrations of simple Lie algebras are classified by $2$-cocycles, due again to the vanishing of the symmetric part of the second cohomology group.Comment: 26 pages, standard LaTeX2

Does Scenic Make Cents?

The stretch of California Route One (Highway 1) from the City of San Luis Obispo reaching north to the Monterey County line is one of the most scenic drives in the United States. This stretch of highway is a destination in its own right; so much so, the San Luis Obispo North Coast Scenic Byway is federally designated as an All-American Road, the highest scenic designation of any road or highway in the nation. There has been a history for funding the preservation and enhancement of these roads; however, it was removed in 2012. Even with the lack of current funding opportunities, the San Luis Obispo Council of Governments (SLOCOG) continues to recognize the importance of the corridor in attracting valuable tourism revenue thus commissioning this update and economic analysis. Through the economic analysis it was found that visitor spending in the byway region increased by 23% from over $500 million in 2006 to almost$656 million in 2012. In 2012, visitor spending related associated with scenic recognition and enhancement projects along the corridor was about $217,000 in direct revenue. As a result of research, outreach, and data analysis, this project did find that being scenic does make “cents.

Interview with Lee Walker

Lee Walker talks about his job in the Knox County Soil and Water Conservation Districthttps://digital.kenyon.edu/lak_interviews/1032/thumbnail.jp

Interview with Jim Gibson

Jim Gibson talks about the history of Knox Countyhttps://digital.kenyon.edu/lak_interviews/1030/thumbnail.jp

Interview with Mayor Richard Mavis

Richard Mavis talks about the Knox County Communityhttps://digital.kenyon.edu/lak_interviews/1031/thumbnail.jp

Minimum Tillage Corn Trial

Minimum tillage practices have significant potential to reduce expenses and the potential negative environmental effects caused by intensive tillage operations. Conventional tillage practices require heavy machinery to work and groom the soil surface in preparation for the planter. The immediate advantage of reduced tillage for the farm operator is less fuel expense, equipment, time, and labor required. It’s also clear that intensive tillage potentially increases nutrient and soil losses to our surface waterways. By turning the soil and burying surface residue, more soil particles are likely to detach from the soil surface and increase the potential for run off from agricultural fields. Reducing the amount and intensity of tillage can help build soil structure and reduce soil erosion

Trust Development in Research with Indigenous Communities in the United States

A historical backdrop of oppression and exploitation has set the stage for distrust in research relationships with many indigenous communities. Although distrust poses a barrier to conducting research with indigenous communities, it also provides a distinct opportunity to examine factors related to trust development. Therefore, the purpose of this article is to understand the factors that relate to trust development in research relationships with indigenous communities in the United States. This qualitative descriptive study explored the experiences of 13 indigenous and non-indigenous researchers working with indigenous communities. Historical oppression, risk and reputation, power balancing across multiple levels, reciprocity and benevolence, and cross-cultural collaboration were emergent themes related to trust development with indigenous communities. Activities between researchers and indigenous communities occurred within a broader context of historical oppression and were on a continuum between trust-building and trust-breaking