Related papers: Complex and real ranks of reducible cubics

The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computable reducibility hierarchy, comparing and contrasting it with…

Let $k$ be a perfect field of characteristic $p > 2$, and let $K$ be a finite totally ramified extension over $W(k)[\frac{1}{p}]$. Let $R_0$ be an unramified relative base ring over $W(k)\langle X_1^{\pm 1}, \ldots, X_d^{\pm 1}\rangle$, and…

We identify the category of real mixed Hodge structures with the category of vector bundles with connections (not necessarily flat) on C, equivariant with respect to C^*. Here C is the complex plane considered as a 2-dimensional real…

The aim of this paper is to give an alternative proof of Kac's theorem for weighted projective lines (\cite{W}) over the complex field. The geometric realization of complex Lie algebras arising from derived categories (\cite{XXZ}) is…

We prove a number of fundamental facts about the canonical order on projections in C*-algebras of real rank zero. Specifically, we show that this order is separative and that arbitrary countable collections have equivalent (in terms of…

In this paper, we study properties of nodal orders defined over arbitrary base fields. In particular we give a classification of complete real nodal orders.

In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.

Let $X$ be a complex projective variety defined over $\mathbb R$. Recently, Bernardi and the first author introduced the notion of admissible rank with respect to $X$. This rank takes into account only decompositions that are stable under…

The article aims at describing all covers of any finitely generated variety of cBCK-algebras. It is known that subdirectly irreducible cBCK-algebras are rooted trees (concerning their order). Also, all subdirectly irreducible members of…

We obtained some sufficient and necessary conditions of existence of faithful irreducible representations of a soluble group $G$ of finite rank over a field $k$. It was shown that the existence of such representations strongly depends on…

In this paper, we describe the irreducible representations in category O of the rational Cherednik algebra H_c(G_12,h) associated to the complex reflection group G_12 with reflection representation h for an arbitary complex parameter c. In…

We survey some results on real rational surfaces focused on their topology and their birational geometry.

We extend results from an earlier paper giving reconstruction results for the endomorphism monoid of the rational numbers under the strict and reflexive relations to the first order reducts of the rationals and the corresponding…

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

The infinite dimensional Clifford Algebra has a maze of irreducible unitary representations. Here we determine their type -real, complex or quaternionic. Some, related to the Fermi-Fock representations, have no real or quetrnionic…

We give a complete classification (up to isomorphism) of Lie conformal algebras which are free of rank two as $\C[\partial]$-modules, and determine their automorphism groups.

This paper studies modular forms of rank four and level one. There are two possiblities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we…

We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of…

We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version…

We consider sentence-definable and diagram-definable subfamilies of given families of theories, calculi for these subfamilies, as well dynamics and characteristics of these subfamilies with respect to rank and degree.