Related papers: On actions on cubic stochastic matrices
We develop a new, group-theoretic approach to bounding the exponent of matrix multiplication. There are two components to this approach: (1) identifying groups G that admit a certain type of embedding of matrix multiplication into the group…
Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete group on a locally compact Hausdorff topological space,…
We study actions of pointed Hopf algebras on matrix algebras. Our approach is based on known facts about group gradings of matrix algebras.
We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
We present the operator semigroups approach to first- and second-order dynamical systems taking place on metric graphs. We briefly survey the existing results and focus on the well-posedness of the problems with standard vertex conditions.…
We obtain a version of the theorem of the square and a local structure result for actions of connected algebraic groups on seminormal varieties in characteristic 0, and arbitrary varieties in positive characteristics.
Nonlinear matrix equations play a crucial role in science and engineering problems. However, solutions of nonlinear matrix equations cannot, in general, be given analytically. One standard way of solving nonlinear matrix equations is to…
For every variety of algebras and every algebras in these variety we can consider an algebraic geometry. Algebras may be many sorted (not necessarily one sorted) algebras. A set of sorts is fixed for each variety. This theory can be applied…
We define computational atoms named "actions" equipped primarily with three operations: reduction, collection, and inspection. We show how actions can be used for decision-making algorithms from simple axioms. We describe the encodings of…
We initiate the study of group actions on (possibly infinite) semimatroids and geometric semilattices. To every such action is naturally associated an orbit-counting function, a two-variable "Tutte" polynomial and a poset which, in the…
The representation problem of finite-dimensional Markov matrices in Markov semigroups is revisited, with emphasis on concrete criteria for matrix subclasses of theoretical or practical relevance, such as equal-input, circulant, symmetric or…
We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study…
We construct a collection of numerical invariants for approximately transitive (AT) actions (of $\Z$). We use them (sometimes supplemented by other invariants to show that members of various one-parameter families of AT actions are mutually…
We investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group…
For two classes of bisexual populations we give a constructive description of quadratic stochastic operators which act to the Cartesian product of standard simplexes. We consider a bisexual population such that the set of females can be…
We consider actions of a group or a semigroup on a set, which generalize the setup of discrete logarithm based cryptosystems. Such cryptographic group actions have gained increasing attention recently in the context of isogeny-based…
Following the ideas of [AGG11] about Zt x Z2,2-cocyclic Hadamard matrices, we introduce the notion of diagram, which visually represents any set of coboundaries. Diagrams are a very useful tool for the description and the study of paths and…
We develop a theory of twisted actions of categorical groups using a notion of semidirect product of categories. We work through numerous examples to demonstrate the power of these notions. Turning to representations, which are actions that…
Examples of SL(2, Z) actions on differential graded categories are defined and explored.