Related papers: On the geometry of tensor products over finite fie…
The problem of whether the cohomological support map of a finite dimensional Hopf algebra has the tensor product property has attracted a lot of attention following the earlier developments on representations of finite group schemes. Many…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples,…
This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in $\mathbb{R}^9$. The algebraic structure of the tensors and their projections on…
We develop a theory of measures, differential forms and Fourier tramsforms on some infinite-dimensional real vector spaces by generalizing the following two constructions: (a) The construction of the semiinfinite wedge power of a Tate…
The main goal of this paper is to study the class of algebras for which the global dimension of the endomorphism ring of the generator-cogenerator, given by the sum of the projective and injective modules, is equal to three. We will refer…
We describe new theories of composite vector and tensor (p-form) gauge fields made out of zero-dimensional constituent scalar fields (``primitives''). The local gauge symmetry is replaced by an infinite-dimensional global Noether symmetry…
In this paper, we introduce the Grassmann tensor by tensor product of vectors and some basic terminology in tensor theory. Some basic properties of the Grassmann tensors are investigated and the tensor language is used to rewrite some…
In order to study tensor fields of type (0,2) on manifolds and fibrations we introduce the notion of s-spaces. With the help of these objects we generalized the concept of natural tensor without making use of the theory of natural operators…
We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…
We review some important facts about the structure of tensor products of finite dimensional representations of quantum affine algebras. This is done from the elementary standpoint of the representation theory of semisimple Lie algebras in…
We develop finite element spaces of symmetric tensor products of two-forms with polynomial coefficients. In three dimensions, these give higher order finite element spaces of matrix fields with normal-normal continuity, which have…
We study local algebras, which are structures similar to $\mathbb{Z}$-graded algebras concentrated in degrees $-1,0,1$, but without a product defined for pairs of elements at the same degree $\pm1$. To any triple consisting of a Kac-Moody…
Two types of finite element spaces on a tetrahedron are constructed for divdiv conforming symmetric tensors in three dimensions. The key tools of the construction are the decomposition of polynomial tensor spaces and the characterization of…
In this paper we introduce and study a twisted tensor product construction of nonlocal vertex algebras. Among the main results, we establish a universal property and give a characterization of a twisted tensor product. Furthermore, we give…
Tensor hierarchy algebras constitute a class of non-contragredient Lie superalgebras, whose finite-dimensional members are the "Cartan-type" Lie superalgebras in Kac's classification. They have applications in mathematical physics,…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
We study the irreducible decomposition under Sp(2n, R) of the space of torsion tensors of almost symplectic connections. Then a description of all symplectic quadratic invariants of torsion-like tensors is given. When applied to a manifold…
We show that subsingular vectors exist in Verma modules over W(2,2), and present a subquotient structure of these modules. We prove conditions for irreducibility of a tensor product of intermediate series module with the highest weight…
We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new…