Related papers: A Monstrous Proposal

The paper presents a counterexample to the Hodge conjecture.

We show that any normal algebraic monoid is an extension of an abelian variety by a normal affine algebraic monoid. This extends (and builds on) Chevalley's structure theorem for algebraic groups.

In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras.…

This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.

In math.CO/0109093 the author obtained a formula for the value of an irreducible symmetric group character indexed by a partition of rectangular shape. In the present paper this formula is (conjecturally) generalized to arbitrary shapes.

In a recent paper, the authors introduced the notion of an alternating snake and a corresponding family of finite dimensional modules for the quantum affine algebra associated to $A_n$. We prove that under some restrictions, an alternating…

We prove a conjecture of R. Schwartz about the type of some complex hyperbolic triangle groups.

This is the fourth one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups of minus type.

Understanding invertibility in restricted mis\`ere play has been challenging; in particular, the possibility of non-conjugate inverses posed difficulties. Advances have been made in a few specific universes, but a general theorem was…

We characterize relatively hyperbolic groups whose reduced $C^*$-algebra is simple as those, which have no non-trivial finite normal subgroups.

The Mordell-Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of…

In this paper, we propose the study of a conjecture whose affirmative solution would provide an example of a non-convex Chebyshev set in an infinite-dimensional real Hilbert space.

The hypothetical existence of a good theory of mixed motives predicts many deep phenomena related to algebraic cycles. One of these, a generalization of Bloch's conjecture says that "small Hodge diamonds" go with "small Chow groups".…

It is shown that a nontrivial normal subgroup $N$ of a group $G$ is a free factor of the $N$'s normal closure in the $G$'s free product with arbitrary nontrivial groups.

The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of…

We study simple superfaithful and superconnected quandles and we found counterexamples to a conjecture suggested by computational data. We provide also examples of superconnected quandles built using group theoretical results and…

Recently, Moret\'o and Rizo proposed a conjecture, known as the Picky Conjecture, proposing new character correspondences extending the McKay Conjecture. We prove the Picky Conjecture for all quasi-simple groups of Lie type for non-defining…

We consider Majorana algebras generated by three Majorana axes $a_0$, $a_1$ and $a_2$ such that $a_0$ and $a_1$ generate a dihedral algebra of type 2A. We show that such an algebra must occur as a Majorana representation of one of 27…

We consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free…

The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.