Related papers: Weighted surface algebras: general version
A {\em $k$-trinitary algebra} is any subalgebra of the space of smooth functions $f: M \to {\mathbb R}$ that is distinguished in this space by $k$ independent conditions of the form $f(x_i) = f(\tilde x_i) = f(\hat x_i)$, where $x_i, \tilde…
We construct a family of general type surfaces with $q=4$, $p_g=6$ and $K^2=24$. These surfaces enjoy some interesting properties: they are Lagrangian in their Albanese variety and their canonical map is $2:1$ onto a degree $12$ surface in…
In this study we give definitions and characterizations of transversal surfaces of timelike ruled surfaces. We study some special cases such as the striction curve is a geodesic, an asymptotic line or a line of curvature. Moreover, we…
In this study, we give weighted mean and weighted Gaussian curvatures of two types of timelike general rotational surfaces with non-null plane meridian curves in four-dimensional Minkowski space E^4_1 with density…
We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the…
If A is a finite-dimensional symmetric algebra, then it is well-known that the only silting complexes in $\mathrm{K^b}(\mathrm{proj}A)$ are the tilting complexes. In this note we investigate to what extent the same can be said for weakly…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
We prove that globally subanalytic nonsingular CMC surfaces of $\mathbb{R}^3$ are only planes, round spheres or right circular cylinders
The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
We consider two algebras of curves associated to an oriented surface of finite type - the cluster algebra from combinatorial algebra, and the skein algebra from quantum topology. We focus on generalizations of cluster algebras and…
We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of…
We introduce the notion of a standard weighted graph and show that every weighted graph has an essentially unique standard model. Moreover we classify birational transformations between such models. Our central result shows that these are…
A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
We prove that quadratic regular algebras of global dimension three on degree-one generators are related to graded skew Clifford algebras. In particular, we prove that almost all such algebras may be constructed as a twist of either a…
We investigate objects in symmetric tensor categories that have simultaneously finite symmetric and finite exterior algebra. This forces the characteristic of the base field to be $p>0$, and the maximal degree of non-vanishing symmetric and…