Related papers: Minimal clones with weakly abelian representations
We show that any abelian variety that is not affine has a nontrivial strongly abelian subvariety. In later papers in this sequence we apply this result to the study of minimal abelian varieties.
In this article we introduce the notion of weak identities in a group and study their properties. We show that weak identities have some similar properties to ordinary ones. We use this notion to prove that any finitely generated solvable…
We describe a weak tracial analog of approximate representability under the name "weak tracial approximate representability" for finite group actions. Let $G$ be a finite abelian group, let $A$ be an infinite-dimensional simple unital…
We prove that non-trivial representations of the alternating group $A_n$ are reducible over a primitive proper subgroup which is isomorphic to some alternating group $A_m$.
We characterize minimal clones generated by a majority function containing at most seven ternary operations.
A group is small if it has countably many complete $n$-types over the empty set for each natural number n. More generally, a group $G$ is weakly small if it has countably many complete 1-types over every finite subset of G. We show here…
We introduce a weak division-like property for noncommutative rings: a nontrivial ring is fadelian if for all nonzero $a,x$ there exist $b,c$ such that $x=ab+ca$. We prove properties of fadelian rings, and construct examples of such rings…
We discuss a certain class of absolutely irreducible group representations that behave nicely under the restriction to normal subgroups and subalgebras. These representations proved to be useful for the construction of abelian varieties…
In this paper, a group is called weakly amenable if its left regular representation is not uniformly isolated from the trivial representation. First examples of finitely generated non-amenable weakly amenable groups are constructed.
We classify binary minimal clones into seven categories: affine algebras, rectangular bands, $p$-cyclic groupoids, spirals, non-Taylor partial semilattices, melds, and dispersive algebras. Each category has nice enough properties to…
We introduce the notion of the weak tracial approximate representability of a discrete group action on a unital $C^*$-algebra which could have no projections like the Jiang-Su algebra $\mathcal{Z}$. Then we show a duality between the weak…
Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy…
In this note, we prove that if G is a countable group that contains a nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G are weakly isomorphic.
We show that a minimal ideal of a finite-dimensional Lie algebra is either simple or abelian.
In 1986, the second author classified the minimal clones on a finite universe into five types. We extend this classification to infinite universes and to multiclones. We show that every non-trivial clone contains a "small" clone of one of…
We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.
Universal algebra and clone theory have proven to be a useful tool in the study of constraint satisfaction problems since the complexity, up to logspace reductions, is determined by the set of polymorphisms of the constraint language. For…
We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of…
We prove that negative K-groups of small abelian categories are trivial.
In the recent paper [A14], a geometric realization to minimal representations of simple real Lie groups of non Hermitian type is given, based on the geometric setting introduced in [A11]. We give in this paper a geometric realization to…