Related papers: Minimal clones with weakly abelian representations

We study holonomy representations admitting a pair of supplementary faithful sub-representations. In particular the cases where the sub-representations are isomorphic respectively dual to each other are treated. In each case we have a…

This paper aims to characterize the minimal dimensions and super-dimensions of faithful representations for the Heisenberg Lie superalgebras over an algebraically closed field of characteristic zero.

It has recently been shown that a minimal reversible nonsymmetric ring has order 256 answering a questioned original posed in a paper on a taxonomy of 2-primal rings. Answers to similar questions on minimal rings relating to this taxonomy…

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

In this paper, we shall study existence of weak solutions to complex Hessian equations. With appropriate assumptions, it is possible to obtain weak solutions in pluripotential sense.

We prove the existence of a regular semigroup F(X) weakly generated by X such that all other regular semigroups weakly generated by X are homomorphic images of F(X). The semigroup F(X) is introduced by a presentation and the word problem…

We show that a complex structure on a nilpotent almost abelian real Lie algebra is unique if it exists. As a consequence, we get full control over the cohomology and deformations of almost abelian complex nilmanifolds.

In a remarkable article Ribet showed how to attach rational $2$-dimensional representations to elliptic ${\mathbb Q}$-curves. An abelian variety $A$ is a (weak) $K$-variety if it is isogenous to all of its $\text{Gal}_K$-conjugates. In this…

Characterizations of "almost associative" binary operations generating a minimal clone are given for two interpretations of the term "almost associative". One of them uses the associative spectrum, the other one uses the index of…

We give a characterization of the minimal tropical half-spaces containing a given tropical polyhedron, from which we derive a counter example showing that the number of such minimal half-spaces can be infinite, contradicting some statements…

For maximal compact subgroups of the metaplectic group, the minimal types in the Schr\"odinger model of the Weil representation are calculated explicitly. Although these types are known in the case of odd residual characteristic, this…

Small representations of a group bring us to large symmetries in a representation space. Analysis on minimal representations utilises large symmetries in their geometric models, and serves as a driving force in creating new interesting…

Let $G$ be a locally compact abelian group with Pontraygin dual $\widehat{G}$. Suppose $P$ is a closed subsemigroup of $G$ containing the identity element $0$. We assume that $P$ has dense interior and $P$ generates $G$. Let…

We refine the Morgan's work on mixed Hodge structures on Sullivan's $1$--minimal models by using non-abelian Hodge theory. As an application, we give explicit representatives of real unipotent variations of mixed Hodge structures over…

It is shown that the complex field equipped with the "approximate exponential map", defined up to ambiguity from a small group, is quasiminimal: every automorphism-invariant subset of the field is countable or co-countable. If the ambiguity…

In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

An abelian fibration is a proper projective surjective map of complex varieties with general fiber an abelian variety. Consider a multiple fiber of an abelian fibration, and let $m_1, ..., m_k$ be the multiplicities of its irreducible…

We study the accessibility properties of trivial cofibrations and weak equivalences in a combinatorial model category and prove an estimate for the accessibility rank of weak equivalences. In particular, we show that the class of weak…

In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously, showing and demonstrating the main…