相关论文: 2-unitary Operads of GK-dimension 3

We calculate the moments of the Meyer-K\"onig and Zeller operators in terms of elementary functions and polylogarithms.

We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.

We explore algebraic characterizations of 2-knots whose associated knot manifolds fibre over lower-dimensional orbifolds, and consider also some issues related to the groups of higher-dimensional fibred knots.

All deformations of two dimensional centrally extended Galilei group are classified. The corresponding quantum Lie algebras are found.

We study the enumerative geometry of orbits of multidimensional toric action on projective algebraic varieties and develop a new cyclic differential-graded operad, conjecturally governing the real version of the enumerative geometry of…

Let $\mathcal{S}\subset \mathcal{L}^2 \subset \mathcal{S}^*$ be the Gel'fand triple over the Bernoulli space, where elements of $\mathcal{S}^*$ are called Bernoulli generalized functionals. In this paper, we define integrals of Bernoulli…

In this paper we study genus 2 function fields K with degree 3 elliptic subfields. We show that the number of Aut(K)-classes of such subfields of K is 0,1,2, or 4. Also we compute an equation for the locus of such K in the moduli space of…

We provide an angular parametrization of the special unitary group $\textrm{SU}(2^{n})$ generalizing Euler angles for $\textrm{SU}(2)$ by successively applying the KAK decomposition. We then determine constraint equations for the parametric…

It is clarified how cohomologies and Gerstenhaber algebras can be associated with linear pre-operads (comp algebras). Their relation to mechanics and operadic physics is concisely discussed.

We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.

We classify kinematical Lie algebras in dimension 2+1. This is approached via the classification of deformations of the static kinematical Lie algebra. In addition, we determine which kinematical Lie algebras admit invariant symmetric inner…

Groebner-Shirshov basis and Gelfand-Kirillov dimension of the Leavitt path algebra are derived.

This paper describes a higher-categorical version of the theory of colored operads, giving applications to the study of commutative ring spectra.

Let $u(K)$ and $g(K)$ denote the unknotting number and the genus of a knot $K$, respectively. For a 3-braid knot $K$, we show that $u(K)\le g(K)$ holds, and that if $u(K)=g(K)$ then $K$ is either a 2-braid knot, a connected sum of two…

A knot semigroup is defined by A. Vernitski. A. Vernitski conjectured that the knot semigroup of the 2-bridge knot is isomorphic to an alternating sum semigroup. To support this conjecture, and as a first main result, we prove that the knot…

In this paper we consider successive iterations of the first-order differential operations in space ${\bf R}^3.$

In the "6D treatment of Special Relativity" proposed by Igor A. Urusovskii one deals with universal light-like motion of matter pre-elements in the extended (3+3) space and with their regular rotation in the additional 3-space. On the other…

We introduce and study the class of unbounded DunfordPettis operators. As consequences, we give basic properties and derive interesting results about the duality, domination problem and relationship with other known classes of operators.

We establish a sharpening of Kirillov's lemma on nilpotent Lie algebras with 1-dimensional center and use it to study the structure of 3-step nilpotent Lie algebras.

We complete the classification of the pointed Hopf algebras with finite Gelfand-Kirillov dimension that are liftings of the Jordan plane over a nilpotent-by-finite group, correcting the statement in arXiv:1512.09271.