Related papers: Homomorphisms of the alternating group A_5 into a …

Let $G$ be a connected complex Lie group. A real form of $G$ is a closed subgroup $H\subset G$ whose Lie algebra $\mathfrak{h}$ is a real form of the Lie algebra $\mathfrak{g}$ of $G$. A pair $(G,H)$ of this type is reductive, and the…

Classes of $G$-Hom-associative algebras are constructed as deformations of $G$-associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom-Lie algebras as deformations of associative and Lie…

Let K be the kernel of an epimorphism G -> Z, where G is a finitely presented group. If K has infinitely many subgroups of index 2, 3, or 4, then it has uncountably many. Moreover, if K is the commutator subgroup of a classical knot group…

The main result of this paper shows that, over large enough fields of characteristic different from $2$, the alternating Hecke algebras are $\mathbb{Z}$-graded algebras that are isomorphic to fixed-point subalgebras of the quiver Hecke…

A homomorphism from a graph G to a graph H is a function from the vertices of G to the vertices of H that preserves edges. A homomorphism is surjective if it uses all of the vertices of H and it is a compaction if it uses all of the…

A group homomorphism eta:H-->G is called a localization of H if every homomorphism phi:H-->G can be `extended uniquely' to a homomorphism Phi:G-->G in the sense that Phi eta=phi. Libman showed that a localization of a finite group need not…

To classify the finite dimensional pointed Hopf algebras with Weyl group $G$ of $E_8$, we obtain the representatives of conjugacy classes of $G$ and all character tables of centralizers of these representatives by means of software GAP. In…

We show that the topological conjugacy relation of diffeomorphisms on any manifold of dimension at least 2 is not classifiable by countable structures. This answers a question of Foreman and Gorodetski. We also prove that $E_0$ is reducible…

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…

Counterexamples to the Modular Isomorphism Problem were discovered recently. These are non-isomorphic finite $2$-groups $G$ and $H$ that have isomorphic group algebras over the field $\mathbb{Z}/2\mathbb{Z}$ and non-isomorphic group…

In this paper we classify the finite groups satisfying the following property $P_4$: their orders of representatives are set-wise relatively prime for any 4 distinct non-central conjugacy classes.

Let $G$ be a linear algebraic group over a field $k$ of characteristic 0. We show that any two connected semisimple $k$-subgroups of $G$ that are conjugate over an algebraic closure of $k$ are actually conjugate over a finite field…

Let $G$ be a finite group. There is a standard theorem on the classification of $G$-equivariant finite dimensional simple commutative, associative, and Lie algebras (i.e., simple algebras of these types in the category of representations of…

We show that for any countable homogeneous ordered graph $G$, the conjugacy problem for automorphisms of $G$ is Borel complete. In fact we establish that each such $G$ satisfies a strong extension property called ABAP, which implies that…

Let $IET(\mathbb{S}^{1})$ be the group of interval exchange transformation of $\mathbb{S}^{1}$ and $\mathcal{AC}_{+}(\mathbb{S}^{1})$ be the group of absolutely continuous preserving orientation bijection with inverse absolutely continuous.…

In this note, starting with any group homomorphism $f\colon\Gamma\to G$, which is surjective upon abelianization, we construct a universal central extension $u\colon U\twoheadrightarrow G,$ UNDER $\Gamma$ with the same surjective property,…

We study a class of $\Z^{d}$-substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of $\Z^{d}$. We prove that any measurable factor map and even…

A collection C of subgroups of a finite group G can give rise to three different standard formulas for the cohomology of G in terms of either: the subgroups in C; or their centralizers; or their normalizers. We give a short but systematic…

Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf subalgebra of E, H is a subcoalgebra in E…

In this paper, we compute the number of distinct centralizers of some classes of finite rings. We then characterize all finite rings with $n$ distinct centralizers for any positive integer $n \leq 5$. Further we give some connections…