Related papers: Subdirectly irreducible medial quandles
The aim of this paper is to propose a theory of derivations for quandles. Given a quandle $A$ admitting an action by a quandle $Q$, derivations from $Q$ to $A$ are introduced as twisted analogues of quandle homomorphisms. It is shown that…
We classify extremal divisorial contraction which contracts a divisor to a curve from a smooth fourfold. We prove the exceptional divisor is $\Bbb P^2$bundle or quadric bundle over a smooth curve and the contraction is the blowing up along…
We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…
A subvariety of a quasi-projective complex variety $X$ is called ``universally irreducible'' if its preimage inside the universal cover of $X$ is irreducible. In this paper we investigate sufficient conditions for universal irreducibility.…
We obtain a description of the irreducible representation algebra of the alternating group of degree four over the ring of 2-adic integers.
We show that the fundamental quandle defines a functor from the oriented tangle category to a suitably defined quandle category. Given a tangle decomposition of a link $L$, the fundamental quandle of $L$ may be obtained from the fundamental…
We produce an example of an irreducible discrete subgroup in the product $SL(2,\R)\times SL(2,\R)$ which is not a lattice. This answers a question asked in [15].
We complete a classification of the two-vertex geometrically irreducible algebras. We also classify the algebras in new classes of hom- and ext-irreducible algebras.
Non-classical virtual knots may have non-isomorphic upper and lower quandles. We exploit this property to define the quandle difference invariant, which can detect non-classicality by comparing the numbers of homomorphisms into a finite…
Gentle algebras are in bijection with admissible dissections of marked oriented surfaces. In this paper, we further study the properties of admissible dissections and we show that silting objects for gentle algebras are given by admissible…
We classify all conformal irreducible modules of finite type over the Cheng Kac superalgebra CK(6).
It is shown that nodal sequences determine the underlying manifold up to scaling within classes of rectangles with Dirichlet boundary conditions, separable two dimensional tori, two-dimensional flat Klein bottles and flat tori in two and…
We develop some general ideas to study connected quandles of prime power size and we classify non-affine connected quandles of size $p^3$ for $p>3$, using a combination of group theoretical and universal algebraic tools. As a byproduct we…
We complete the classification of hyperelliptic threefolds, describing in an elementary way the hyperelliptic threefolds with group $D_4$. These are algebraic and form an irreducible 2-dimensional family. Our paper is fully self-contained.
In this article we classify indecomposable objects of the derived categories of finitely-generated modules over certain infinite-dimensional algebras. The considered class of algebras (which we call nodal algebras) contains such well-known…
We describe degenerations of three-dimensional Jordan superalgebras over $\mathbb{C}$. In particular, we describe all irreducible components in the corresponding varieties.
Quandle coloring quivers are directed graph-valued invariants of oriented knots and links, defined using a choice of finite quandle $X$ and set $S\subset\mathrm{Hom}(X,X)$ of endomorphisms. From a quandle coloring quiver, a polynomial knot…
We generalize the notion of biquandles to psyquandles and use these to define invariants of oriented singular links and pseudolinks. In addition to psyquandle counting invariants, we introduce Alexander psyquandles and corresponding…
In this paper we investigate the class of semimedial left quasigroups, a class that properly contains racks and medial left quasigroups. We extend most of the results about commutator theory for racks collected in \cite{CP} and some of the…
We define a new class of racks, called finitely stable racks, which, to some extent, share various flavors with Abelian groups. Characterization of finitely stable Alexander quandles is established. Further, we study twisted rack dynamical…