Related papers: Commuting matrices via commuting endomorphisms

We investigate the computational complexity of the problem of deciding if an algebra homomorphism can be factored through an intermediate algebra. Specifically, we fix an algebraic language, L, and take as input an algebra homomorphism f…

Motivated in part by representation theoretic questions, we prove that if G is a finite quasi-simple group, then there exists an elementary abelian subgroup of G that intersects every conjugacy class of involutions of G.

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

We study the mapping class group of a nontrivial irreducible shift of finite type: the group of flow equivalences of its mapping torus modulo isotopy. This group plays for flow equivalence the role that the automorphism group plays for…

If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the…

The group isomorphism problem asks whether two given groups are isomorphic or not. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of isomorphism…

We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…

The problem of deciding, given a complex variety X, a point x in X, and a subvariety Z of X, whether there is an automorphism of X mapping x into Z is proved undecidable. Along the way, we prove the undecidability of a version of Hilbert's…

We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…

The functor that takes a ring to its category of modules has an adjoint if one remembers the forgetful functor to abelian groups: the endomorphism ring of linear natural transformations. This uses the self-enrichment of the category of…

Computational problems concerning the orbit of a point under the action of a matrix group occur throughout computer science, including in program analysis, complexity theory, quantum computation, and automata theory. In many cases the focus…

Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of…

The isomorphism problem means to decide if two given finite-dimensional simple algebras over the same centre are isomorphic and, if so, to construct an isomorphism between them. A solution to this problem has applications in computational…

Let $\mathcal{A}_g$ be the moduli space of principally polarized abelian varieties. We study the problem of counting the number of principal polarizations modulo the natural action of the automorphism group of the abelian variety on a very…

Let $\mathcal{A}$ be an abelian variety over a number field, with a good reduction at a prime ideal containing a prime number $p$. Denote by ${\rm A}$ an abelian variety over a finite field of characteristic $p$, obtained by the reduction…

We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at…

Pairings are particular bilinear maps, and as any bilinear maps they factor through the tensor product as group homomorphisms. Besides, nothing seems to prevent us to construct pairings on other abelian groups than elliptic curves or more…

We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed…

Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more…

We consider the problem of enumeration of planar maps and revisit its one-matrix model solution in the light of recent combinatorial techniques involving conjugated trees. We adapt and generalize these techniques so as to give an…