Related papers: The octonionic projective plane

We compute some numerical invariants of the lines on hyperplane sections of a smooth cubic threefold over complex numbers. We also prove that for any smooth hypersurface $X\subset \mathbb P^{n+1}$ of degree $d$ over an algebraically closed…

Numerical tools for computation of $\wp$-functions, also known as Kleinian, or multiply periodic, are proposed. In this connection, computation of periods of the both first and second kinds is reconsidered. An analytical approach to…

We propose a construction of the spherical subalgebra of a symplectic reflection algebra of an arbitrary rank corresponding to a star-shaped affine Dynkin diagram. Namely, it is obtained from the universal enveloping algebra of a certain…

In positive characteristic the Jordan plane covers a finite-dimensional Nichols algebra that was described by Cibils, Lauve and Witherspoon and we call the restricted Jordan plane. In this paper the characteristic is odd. The defining…

A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…

We construct an irreducible embedded projective plane in $S^4$. This gives a counterexample to the Kinoshita conjecture and answers Problem 4.37 of the K3 problem list. Moreover, we answer both Questions (i) and (ii) of Problem 4.37: (i)…

In this short article, we state a Hopf type lemma for fractional equations and the outline of its proof. We believe that it will become a powerful tool in applying the method of moving planes on fractional equations to obtain qualitative…

Let $p$ be a prime number. Motivated by the local lifting problem for $(\mathbb{Z}/p\mathbb{Z})^n$ with $n>1$, we prove several new results on certain $\mathbb{F}_p$-vector spaces of logarithmic differential forms on the projective line in…

Let k be an algebraically closed field of characteristic 0 and let D_m be the dihedral group of order 2m with m= 4t, with t bigger than 2. We classify all finite-dimensional Nichols algebras over D_m and all finite-dimensional pointed Hopf…

In this paper we construct and study two new families of finite dimensional pointed Hopf algebras which generalize Radford's families. We show that over any infinite field which contains a primitive nth root of unity, one of the families…

Let $p$ be a polynomial in one variable whose roots either all have multiplicity more than 1 or all have multiplicity exactly 1. It is shown that the universal $C^*$-algebra of a relation $p(x)=0$, $\|x\| \le 1$ is semiprojective. In the…

The connection of (split-)division algebras with Clifford algebras and supersymmetry is investigated. At first we introduce the class of superalgebras constructed from any given (split-)division algebra. We further specify which real…

Let $\mathcal{C}$ be a decomposable plane curve over an algebraically closed field $k$ of characteristic 0. That is, $\mathcal{C}$ is defined in $k^2$ by an equation of the form $g(x) = f(y)$, where $g$ and $f$ are polynomials of degree at…

In this paper, we show that Hennings construction of invariants of framed links and 3-manifolds obtained from Hopf algebras can also be carried out for some algebraic quantum groups.

We show that Stolarsky's invariance principle, known for point distributions on the Euclidean spheres, can be extended to the real, complex, and quaternionic projective spaces and the octonionic projective plane. A part of the results…

Let H be a non-semisimple Hopf algebra of dimension 2p^2 over an algebraically closed field of characteristic zero, where p is an odd prime. We prove that H or H^* is pointed, which completes the classification for Hopf algebras of these…

For each nontrivial semisimple Hopf algebra $H$ of dimension sixteen over $\mathbb{C}$, the smallest dimension inner-faithful representation of $H$ acting on a quadratic AS regular algebra $A$ of dimension 2 or 3, homogeneously and…

In 1960, J.F. Adams introduced secondary cohomology operations that are defined on cohomology elements on which sufficiently many Steenrod algebra elements vanish. This led to his theorem on singly generated cohomology rings, which in turn…

In analogy with the Poisson algebra of the quadratic forms on the symplectic plane, and the notion of duality in the projective plane introduced by Arnold in \cite{Arn}, where the concurrence of the triangle altitudes is deduced from the…

Given a complex algebraic variety X, we define a natural number called the motivic dimension which measures the amount of transcendental (co)homology of X. It is zero precisely when all the (co)homolgy is spanned by algebraic cycles. Most…