Related papers: Algorithmic problems in twisted groups of Lie type

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…

In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…

We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…

People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…

Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later…

This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…

Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of…

In this paper, we propose a unified framework and an algorithm for the problem of group recommendation where a fixed number of items or alternatives can be recommended to a group of users. The problem of group recommendation arises…

This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…

We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum…

Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…

We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…

The main component of (constructive) recognition algorithms for black box groups of Lie type in computational group theory is the construction of unipotent elements. In the existing algorithms unipotent elements are found by random search…

Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. It turns out that Stallings'…

The $K$-means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a $K$-means type algorithm that assigns observations to groups while estimating their skewness-transformation…

We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…

This thesis deals with the conjugacy problem in groups and its twisted variants. We analyze recent results by Bogopolski, Martino, Maslakova and Ventura on the twisted conjugacy problem in free groups and its implication for the conjugacy…

We present a new algorithm that, given two matrices in $GL(n,Q)$, decides if they are conjugate in $GL(n,Z)$ and, if so, determines a conjugating matrix. We also give an algorithm to construct a generating set for the centraliser in…

We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…

I review recent research and advances in algorithms for solvers and gauge generation, with an emphasis on practical algorithms for four dimensional simulations. Particular consideration is given to advances in multigrid solvers, fourier…