Related papers: A remark on automorphisms of tensor spaces
A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we…
A tensor space is a vector space equipped with a finite collection of multilinear forms. The length of a tensor space is its length as a representation of its symmetry group. Infinite dimension tensor spaces of finite length are special,…
A cubic space is a vector space equipped with a symmetric trilinear form. Using categorical Fra\"iss\'e theory, we show that there is a universal ultrahomogeneous cubic space $V$ of countable infinite dimension, which is unique up to…
A vector space is commonly defined as a set that satisfies several conditions related to addition and scalar multiplication. However, for beginners, it may be hard to immediately grasp the essence of these conditions. There are probably a…
The aim of this note is to explain a generalization to the real case of a well known result on the automorphism group of an unbounded tube type symmetric domain in a complex vector space of finite dimension.
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
We introduce the rigid tensor category of tubular partitions, and use it to provide a combinatorial model for the representation category of the quantum automorphism group of a homogeneous rooted tree.
Square matrices represent linear self-maps of vector spaces, and their eigenpoints are the fixed points of the induced map on projective space. Likewise, polynomial self-maps of a projective space are represented by tensors. We study the…
The automorphism group of a one dimensional shift space over a finite alphabet exhibits different types of behavior: for a large class with positive entropy, it contains a rich collection of subgroups, while for many shifts of zero entropy,…
We show that there is an infinite group of special automorphisms of the deformed group of diffeomorphisms, which describes parallel transports in Riemannian spaces of any variable curvature. Generators of translations of such group contain…
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes.…
The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature…
We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…
A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…
Perturbation theory for a class of topological field theories containing antisymmetric tensor fields is considered. These models are characterized by a supersymmetric structure which allows to establish their perturbative finiteness.
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
A finite linear space is a finite set of points and lines, where any two points lie on a unique line. Well known examples include projective planes. This project focuses on linear spaces which admit certain types of symmetries. Symmetries…
The Lie algebra $gl(V)$ is the Lie algebra of all endomorphisms of a countable-dimensional complex vector space $V$. We define a tensor category of topological representations of the Lie algebra $gl(V)$, so that $V$, its dual and the…
We describe all closed permutation groups which act on the set of vectors of a countable vector space $V$ over a prime field of odd order and which contain all automorphisms of $V$. In particular, we prove that their number is finite. These…
For a representation of a finite group $G$ on a complex vector space $V$ we determine when a holomorphic $\binom{p}{q}$-tensor field on the principle stratum of the orbit space $V/G$ can be lifted to a holomorphic $G$-invariant tensor field…