Related papers: Classification of real trivectors in dimension nin…

In this paper we classify real trivectors in dimension 9. The corresponding classification over the field C of complex numbers was done by Vinberg and Elashvili in 1978. One of the main tools used for their classification was the…

In 1981 Antonyan classified the orbits of SL$(8,\mathbb{C})$ on $\bigwedge^4 \mathbb{C}^8$. This is an example of a $\theta$-group action as introduced and studied by Vinberg. The orbits of a $\theta$-group are divided into three classes:…

The division of compact Riemann surfaces into 3 cases K_C<0, g=0, or K_C=0, g=1, or K_C>0, g>=2 is well known, and corresponds to the familiar trichotomy of spherical, Euclidean and hyperbolic non-Euclidean plane geometry. Classification…

Using adjoint representation we firstly classify two and three dimensional Lie super-bialgebras obtain from decomposable Lie superalgebras. In this way we complete the classification obtained by Eghbali et al., [J. Math. Phys. 51, 073503…

A brief proof of Lie's classification of finite dimensional subalgebras of vector fields on the complex plane that have a proper Levi decomposition is given. The proof uses basic representation theory of sl(2, C). This, combined with…

We use the theory of theta-groups developed by Vinberg, along with computations in the computer algebra system GAP4, to classify the orbits of Spin(10,C)x SL(4,C) acting on the tensor product of the half spin module of Spin(10,C) and the…

Let $\mathbb{F}$ be a field of characteristic $\neq 2$ and $3$, let $V$ be a $\mathbb{F}$-vector space of dimension $6$, and let $\Omega \in \wedge ^2V^\ast $ be a non-degenerate form. A system of generators for polynomial invariant…

In this paper, complex vector bundles of rank $r$ over $8$-dimensional spin$^{c}$ manifolds are classified in terms of the Chern classes of the complex vector bundles and the cohomology ring of the manifolds, where $r = 3$ or $4$. As an…

We develop categorical and number theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular categories of rank $8$. In particular we find three distinct…

We discuss the algebraic classification of the Weyl tensor in higher dimensional Lorentzian manifolds. This is done by characterizing algebraically special Weyl tensors by means of the existence of aligned null vectors of various orders of…

Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering…

We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a complete elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We…

We study the geometry of the (generalized) twistor triangles $\triangle J_1J_2J_3$ in the period domain of compact complex tori of complex dimension $2n$ by the means of the representation theory of the algebras (of real dimension 8)…

We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most)…

The classification of complex of real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example the nilpotent Lie algebras are classified only up to the dimension 7. Moreover, to recognize a given…

An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…

In 1994, Dhar and Sinha provided a graphic representation in $\mathbb{R}^{2}$ of the classification of triangles based on similarity. In this article, we briefly recall their treatment and offer a generalization by providing a graphic…

We are interested in the relationship between the virtual cohomological dimension (or vcd) of a discrete group Gamma and the smallest possible dimension of a model for the classifying space of Gamma relative to its family of virtually…

This is a continuation of the authors' previous work [math.AT/9910001] on classification of equivariant complex vector bundles over a circle. In this paper we classify equivariant real vector bundles over a circle with a compact Lie group…

We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over R and C, as well as the classification of the 4-dimensional…