Related papers: Dimensions of finite type for representations of p…
We prove that if a finite group scheme $G$ over a field $k$ has essential dimension one, then it embeds in $PGL_{2/k}$. We use this to give an explicit classification of all infinitesimal group schemes of essential dimension one over any…
A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…
In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
We study poset limits given by sequences of finite interval orders or, as a special case, finite semiorders. In the interval order case, we show that every such limit can be represented by a probability measure on the space of closed…
We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.
We examine situations, where representations of a finite-dimensional $F$-algebra $A$ defined over a separable extension field $K/F$, have a unique minimal field of definition. Here the base field $F$ is assumed to be a $C_1$-field. In…
For first-order expansions of the field of real numbers, nondefinability of the set of natural numbers is equivalent to equality of topological and Assouad dimension on images of closed definable sets under definable continuous maps.
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to…
We define a finite-dimensional partially formal supermanifold as a manifold having $q$ odd coordinates and $k + l$ even coordinates with $l$ of them taking only nilpotent values. We show that this notion can be used to formulate…
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…
In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…
We discuss essential dimension of group schemes, with particular attention to infinitesimal group schemes. We prove that the essential dimension of a group scheme of finite type over a field k is at least equal to the difference between the…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
A partially ordered set P is representable if there is a bounded distributive lattice such that its ordered set of prime ideals is order-isomorphic to P. We show that if the order components of a poset P are representable, then so is P.…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.