Related papers: Deformed graphical zonotopal algebras
Quadratic algebras associated to pseudo-roots of noncommutative polynomials have been introduced by I. Gelfand, Retakh, and Wilson in connection with studying the decompositions of noncommutative polynomials. Later they (with S. Gelfand and…
We will consider P-graph complexes, where P is a cyclic operad. P-graph complexes are natural generalizations of Kontsevich's graph complexes -- for P = the operad for associative algebras it is the complex of ribbon graphs, for P = the…
We study all possible deformations of the Maxwell algebra. In D=d+1\neq 3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1,1)\oplus so(d,1) or to so(d,2)\oplus so(d,1) depending on the signs…
We study the plane automorphisms given by polynomials with certain degree decompositions.
An algebraic deformation theory of coalgebra morphisms is constructed.
We study the Hilbert function and the Hilbert series of the vertex cover algebra $A(G)$, where $G$ is a Cohen-Macaulay bipartite graph.
We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…
We offer a Maple-procedure for computing of the Hilbert polynomials of the algebras of $SL_2$-invariants
We study all possible deformations of the Maxwell algebra. In D=d+1\neq 3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1,1)\oplus so(d,1) or to so(d,2)\oplus so(d,1) depending on the signs…
In this paper we introduce generalized Spencer cohomology for finite depth Z-graded Lie (super)algebras. We develop a method of finding filtered deformations of such Z-graded Lie (super)algebras based on this cohomology. As an application…
We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group $W$ we consider the subalgebra generated by flat…
The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…
We apply the method of orbit harmonics to the set of break divisors and orientable divisors on graphs to obtain the central and external zonotopal algebras respectively. We then relate a construction of Efimov in the context of…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…
We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf algebras. One of our examples is the Fomin-Kirillov algebra FK3. Another one appeared in a paper of Garc\'ia Iglesias and Vay. As a consequence of our…
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
We define and investigate properties of universal operator algebras of directed graphs. Results include free products decomposition and continuity of the construction with respect to direct limits. Lastly we prove some K-theoretic results…
In this paper, we investigate families of singular holomorphic Lie algebroids on complex analytic spaces. We introduce and study a special type of deformation called unfoldings of Lie algebroids, which generalizes the theory of singular…
In this paper we give an effective characterization of Hilbert functions and polynomials of standard algebras over an Artinian equicharacteristic local ring; the cohomological properties of such algebras are also studied. We describe…
We study invariants of virtual graphoids, which are virtual spatial graph diagrams with two distinguished degree-one vertices modulo graph Reidemeister moves applied away from the distinguished vertices. Generalizing previously known…