Related papers: Finite matrix multiplication algorithms from infin…

We consider the low rank matrix completion problem over finite fields. This problem has been extensively studied in the domain of real/complex numbers, however, to the best of authors' knowledge, there exists merely one efficient algorithm…

Any simple Lie superalgebras over the complex field can be constructed from some triple systems. Examples of Lie superalgebras $D(2,1;\alpha)$, G(3) and F(4) are given by utilizing a general construction method based upon $(-1,-1)$ balanced…

Let $\text{U}(n,\mathbb{F}_{q^2})$ denote the subgroup of unitary matrices of the general linear group $\text{GL}(n,\mathbb{F}_{q^2})$ which fixes a Hermitian form and $M\geq 2$ an integer. This is a companion paper to the previous works…

It is shown that there is $N$ such that there is no algorithm to decide for identities in at most $N$ variables validity in the class of finite modular lattices. This is based on Slobodskoi's result that the Restricted Word Problem is…

The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex…

We construct examples of finitely generated decidable group presentations that satisfy certain combinations of solvability for the word problem, solvability for the bounded word problem, and computablity for the Dehn function. We prove that…

Fix a finite group $G$. We study the computational complexity of counting problems of the following flavor: given a group $\Gamma$, count the number of homomorphisms $\Gamma \to G$. Our first result establishes that this problem is…

Obeying constraints imposed by classical physics, we give optimal fine-grained algorithms for matrix multiplication and problems involving graphs and mazes, where all calculations are done in 3-dimensional space. We assume that whatever the…

We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space…

We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the…

We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matrices are automatic. This shows a new relation between two…

We give a partial solution to a long-standing open problem in the theory of quantum groups, namely we prove that all finite-dimensional representations of a wide class of locally compact quantum groups factor through matrix quantum groups…

We study a generalization of the Fuchsian triangle groups to the hyperbolic 3-space, namely, the groups generated by half-turns in three hyperbolic lines. The role of the hyperbolic triangles is now played by the right-angled hexagons. This…

We study the possibility of applying a finite-dimensionality argument in order to address parts of the Baum-Connes conjecture for finitely generated linear groups. This gives an alternative approach to the results of Guentner, Higson, and…

We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum…

We demonstrate that the matrix quantum group $SL_q(2)$ gives rise to nontrivial matrix product operator representations of the Lie group $SL(2)$, providing an explicit characterization of the nontrivial global $SU(2)$ symmetry of the XXZ…

Efficient multiple precision linear numerical computation libraries such as MPLAPACK are critical in dealing with ill-conditioned problems. Specifically, there are optimization methods for matrix multiplication, such as the Strassen…

The (asymptotic) complexity of matrix multiplication (over the complex field) is measured by a real parameter w > 0, called the exponent of matrix multiplication (over the complex field), which is defined to be the smallest real number w >…

We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms.

Products and sums of random matrices have seen a rapid development in the past decade due to various analytical techniques available. Two of these are the harmonic analysis approach and the concept of polynomial ensembles. Very recently, it…