Related papers: Prehomogeneous vector spaces and field extensions …

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…

In this paper we study the analytic properties of a multiple Dirichlet series associated to the prehomogeneous vector space of binary cubic forms.

We investigate the second cohomology space of the Lie superalgebra $\mathcal{K}(2)$ with coefficients in the superspace of weighted densities on the (1,2)-dimentional real superspace. We explicitly give cocycles spanning this cohomology…

Let $L/K$ be any finite Galois extension with Galois group $G$. It is known by Chase and Sweedler that the Hopf--Galois correspondence is injective for every Hopf--Galois structure on $L/K$, but it need not be bijective in general.…

We develop geometry-of-numbers methods to count orbits in prehomogeneous vector spaces having bounded invariants over any global field. As our primary example, we apply these techniques to determine, for any base global field $F$, the…

In this paper, we consider the structure of rational orbit of some prehomogeneous vector spaces originally motivated by Wright and Yukie. After we give a refinement of Wright-Yukie's construction, we apply it to the inner forms of the $D_5$…

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups. We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the…

This is a survey on various aspects of the cohomology of the moduli space of abelian varieties

Let H_1=SL(5), H_2=SL(3), H=H_1 \times H_2. It is known that (G,V) is a prehomogeneous vector space (see [22], [26], [25], for the definition of prehomogeneous vector spaces). A non-constant polynomial \delta(x) on V is called a relative…

We compute the p-adic geometric pro-\'etale cohomology of the affine space (in any dimension). This cohomogy is non-zero, contrary to the \'etale cohomology, and can be described by means of differential forms.

Let $M$ be a smooth manifold, $\cal S$ the space of polynomial on fibers functions on $T^*M$ (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space of the Lie algebra, $Vect(M)$, of vector fields on $M$ with…

Let $F$ be a non-Archimedean local field with residue field $k$ of odd characteristic, and let $B/F$ be the division algebra of rank 4. We explicitly construct a stable curve $\mathfrak{X}$ over the algebraic closure of $k$ admitting an…

We study fibred spaces with fibres in a structure category $\V$ and we show that cellular approximation, Blakers--Massey theorem, Whitehead theorems, obstruction theory, Hurewicz homomorphism, Wall finiteness obstruction, and Whitehead…

We determine the set which parametrizes the GIT stratification for four prehomogeneous vector spaces in this paper.

In this article we describe the projective representation of Plesken Lie algebras and equivalent central extensions of these algebras. Further it is also shown that there exists a bijective correspondence between second cohomology group,…

We show that there exists a Galois correspondence between subalgebras of an H-comodule algebra A over a base ring R and generalised quotients of a Hopf algebra H if both A and H are flat Mittag--Leffler modules. We also provide new criteria…

This paper provides an introduction to non-abelian Hodge theory and moduli spaces of Higgs bundles on compact Riemann surfaces. We develop the moduli theory of vector bundles and Higgs bundles, establish the main correspondences of…

We investigate the first cohomology space associated with the embedding of the Lie superalgebra $\cK(2)$ of contact vector fields on the (1,2)-dimensional supercircle $S^{1\mid 2}$ in the Lie superalgebra $\cS\Psi \cD \cO(S^{1\mid 2})$ of…

Let (G, V) be a prehomogeneous vector space, let O be any G(F_q)-invariant subset of V(F_q), and let f be the characteristic function of O. In this paper we develop a method for explicitly and efficiently evaluating the Fourier transform of…

The existence of Hopf fibrations S^{2N+1}/S^1 = CP^N and S^{4K+3}/S^3 = HP^K allows us to treat the Hilbert space of generic finite-dimensional quantum systems as the total bundle space with respectively $U(1)$ and $SU(2)$ fibers and…