Koszul differential graded algebras and BGG correspondence

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul DG algebra $A$ is AS-regular, the Ext-algebra $E$ of $A$ is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence between the stable category of finitely generated left $E$-modules, and the quotient triangulated category of the full triangulated subcategory of the derived category of right DG $A$-modules consisting of all compact DG modules modulo the full triangulated subcategory consisting of all the right DG modules with finite dimensional cohomology. The classical BGG correspondence can derived from the DG version.Comment: 29 page

Solar transition region in the quiet Sun and active regions

The solar transition region (TR), in which above the photosphere the tempera- ture increases rapidly and the density drops dramatically, is believed to play an important role in coronal heating and solar wind acceleration. Long-lasting up-flows are present in the upper TR and interpreted as signatures of mass supply to large coronal loops in the quiet Sun. Coronal bright points (BPs) are local heating phenomena and we found a different Doppler-shift pattern at TR and coronal temperatures in one BP, which might be related to the twisted loop system. The dominant energy loss in the lower TR is the Ly-alpha emission. It has been found that most Ly-alpha radiance profiles are stronger in the blue peak, an asymmetry opposite to higher order Lyman lines. This asymmetry is stronger when the downflow in the middle TR is stronger, indicating that the TR flows play an important role in the line formation process. The peak separation of Ly-alpha is found to be larger in coronal holes than in the quiet Sun, reflecting the different magnetic structures and radiation fields between the two regions. The Lyman line profiles are found to be not reversed in sunspot plume and umbra regions, while they are obviously reversed in the surrounding plage region. At TR temperatures, the densities of the sunspot plume and umbra are a factor of 10 lower than of the plage, indicating that the sunspot plasma emitting at TR temperatures is higher and possibly more extended above sunspots than above the plage region.Comment: This paper has been withdrawn by the author because it's not a referred pape

Cocommutative Calabi-Yau Hopf algebras and deformations

The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a universal enveloping algebra of a finite dimensional Lie algebra \g with a finite subgroup $G$ of automorphisms of \g is Calabi-Yau if and only if the universal enveloping algebra itself is Calabi-Yau and $G$ is a subgroup of the special linear group SL(\g). The Noetherian cocommutative Calabi-Yau Hopf algebras of dimension not larger than 3 are described. The Calabi-Yau property of Sridharan enveloping algebras of finite dimensional Lie algebras is also discussed. We obtain some equivalent conditions for a Sridharan enveloping algebra to be Calabi-Yau, and then partly answer a question proposed by Berger. We list all the nonisomorphic 3-dimensional Calabi-Yau Sridharan enveloping algebras

Individualism-collectivism and interpersonal memory guidance of attention

Recently it has been shown that the allocation of attention by a participant in a visual search task can be affected by memory items that have to be maintained by a co-actor, when similar tasks are jointly engaged by dyads (He, Lever, & Humphreys, 2011). In the present study we examined the contribution of individualism-collectivism to this ‘interpersonal memory guidance’ effect. Actors performed visual search while a preview image was either held by the critical participant, held by a co-actor or was irrelevant to either participant. Attention during search was attracted to stimuli that matched the contents of the co-actor’s memory. This interpersonal effect correlated with the collectivism scores, and was enhanced by priming with a collectivistic scenario. The dimensions of individualism, however, did not contribute to performance. These data suggest that collectivism, but not individualism, modulates interpersonal influences on memory and attention in joint action

Sunward-propagating Alfv\'enic fluctuations observed in the heliosphere

The mixture/interaction of anti-sunward-propagating Alfv\'enic fluctuations (AFs) and sunward-propagating Alfv\'enic fluctuations (SAFs) is believed to result in the decrease of the Alfv\'enicity of solar wind fluctuations with increasing heliocentric distance. However, SAFs are rarely observed at 1 au and solar wind AFs are found to be generally outward. Using the measurements from Voyager 2 and Wind, we perform a statistical survey of SAFs in the heliosphere inside 6 au. We first report two SAF events observed by Voyager 2. One is in the anti-sunward magnetic sector with a strong positive correlation between the fluctuations of magnetic field and solar wind velocity. The other one is in the sunward magnetic sector with a strong negative magnetic field-velocity correlation. Statistically, the percentage of SAFs increases gradually with heliocentric distance, from about 2.7% at 1.0 au to about 8.7% at 5.5 au. These results provide new clues for understanding the generation mechanism of SAFs