Related papers: An efficient quantum algorithm for the hidden subg…

We show that the modular isomorphism problem has a positive answer for groups of nilpotency class 2 with cyclic center, i.e. that for such p-groups G and H an isomorphism between the group algebras FG and FH implies an isomorphism of the…

Identifying symmetries in quantum dynamics, such as identity or time-reversal invariance, is a crucial challenge with profound implications for quantum technologies. We introduce a unified framework combining group representation theory and…

We study solvability, nilpotency and splitting property for algebraic supergroups over an arbitrary field $K$ of characteristic $\mathrm{char}\, K \ne 2$. Our first main theorem tells us that an algebraic supergroup $\mathbb{G}$ is solvable…

If $M$ is a submonoid of a finitely generated nilpotent group $G$, and $MG'$ is a finite index subgroup of $G$, then $M$ itself is a finite index subgroup of $G$. If $MG'=G$, then $M=G$. This generalizes a well-known theorem for subgroups…

Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…

Let $p$ be a prime number and suppose that every maximal subgroup of a finite group is either $p$-nilpotent or has prime index. Such group need not be $p$-solvable, and we study its structure by proving that only one nonabelian simple group…

The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…

The unipotent groups are an important class of algebraic groups. We show that techniques used to compute with finitely generated nilpotent groups carry over to unipotent groups. We concentrate particularly on the maximal unipotent subgroup…

The algebraic diversity framework generalizes temporal averaging over multiple observations to algebraic group action on a single observation for second-order statistical estimation. The central open problem in this framework is…

This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series…

We propose a novel algorithm for selection of dangerous N-2 contingencies associated with line or generator failures. The algorithm is based on iterative filtering of the set of all possible double contingencies. It is certified to identify…

The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based…

This paper gives the first separation of quantum and classical pure (i.e., non-cryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of a celebrated…

We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie…

In this paper, a new key-agreement scheme is proposed and analyzed. In addition to being provably secure in shared secret key indistinguishability model, the scheme has an interesting feature: while using exponentiation over a cyclic…

The Laguerre calculus is widely used for the inversion of differential operators on the Heisenberg group. We extend the Laguerre calculus for nilpotent groups of step two, and test it in the determining of the fundamental solution of the…

We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…

We exhibit an extension of the category of class two nilpotent groups. It has the same objects but, unlike the latter, its morphisms are closed under pointwise addition of maps. At the same time the class of its morphisms is much smaller…

In a recent paper, Kuperberg described the first subexponential time algorithm for solving the dihedral hidden subgroup problem. The space requirement of his algorithm is super-polynomial. We describe a modified algorithm whose running time…

A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…