On some examples of group actions and group extensions

Morava k(s)^* -rings of the extensions of C_p by the products of good groups under diagonal action

This note provides a theorem on good groups in the sense of Hopkins-Kuhn-Ravenel and some relevant examples.

Rognes's theory of Galois extensions and the continuous action of G_n on E_n

Let us take for granted that L_{K(n)}S^0 --> E_n is some kind of a G_n-Galois extension. Of course, this is in the setting of continuous G_n-spectra. How much structure does this continuous G-Galois extension have? How much structure does one want to build into this notion to obtain useful conclusions? If the author's conjecture that ``E_n/I, for a cofinal collection of I's, is a discrete G_n-symmetric ring spectrum" is true, what additional structure does this give the continuous G_n-Galois extension? Is it useful or merely beautiful? This paper is an exploration of how to answer these questi…

On cohomology of split Lie algebra extensions

We introduce the notion of compatible actions in the context of split extensions of finite dimensional Lie algebras over a field. Using compatible actions, we construct a new resolution to compute the cohomology of semi-direct products of Lie algebras. We also give an alternative way to construct the Hochschild-Serre spectral sequence associated to a split extension of finite dimensional Lie algebras and obtain a sharper bound for the length of this spectral sequence.

Green函子的平展扩张示例

Examples of étale extensions of Green functors

本研究将经典平展扩张示例迁移到等变语境，构造了Tambara函子类的Green函子平展扩张新示例，证明了$C_2$-Galois扩张、任意有限$n$的$C_n$-Kummer扩张及一般域平展扩张均可诱导对应Green函子的平展扩张。

Homotopic Hopf-Galois extensions: foundations and examples

Hopf-Galois extensions of rings generalize Galois extensions, with the coaction of a Hopf algebra replacing the action of a group. Galois extensions with respect to a group $G$ are the Hopf-Galois extensions with respect to the dual of the group algebra of $G$. Rognes recently defined an analogous notion of Hopf-Galois extensions in the category of structured ring spectra, motivated by the fundamental example of the unit map from the sphere spectrum to $MU$. This article introduces a theory of homotopic Hopf-Galois extensions in a monoidal category with compatible model category structure that…

四维流形上的非动力学同伦相干作用

Non-kinetic homotopy coherent actions on four-manifolds

该研究给出闭单连通光滑四维流形上二阶非动力学光滑同伦相干作用的首个例子，通过限制离散圆周群在稳定化\(K3\)曲面上的作用获得，还构造相关扩张并展示特殊边界对合，证明了关于整同调球上自由对合光滑扩张的定理。