Related papers: The geometry of polynomial identities

In this paper, we derive eight basic identities of symmetry in three variables related to Euler polynomials and alternating power sums. These and most of their corollaries are new, since there have been results only about identities of…

In this work we consider all metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over \C and \R up to dimension 5 and all metric Lie algebras over \C in dimension 6. We introduce cyclic and reduced cyclic…

We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.

We study the graded polynomial identities with a homogeneous involution on the algebra of upper triangular matrices endowed with a fine group grading. We compute their polynomial identities and a basis of the relatively free algebra,…

Consider a representation $\rho\colon L \to \mathfrak{gl}(V)$ where $L$ is a Lie algebra and $V$ is a finite dimensional vector space. We prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of polynomial…

We provide a topological characterization of quivers whose path algebra satisfies a polynomial identity. This class includes the oriented cycle and acyclic quivers and, in the latter case, we describe the associated T-ideal. We introduce a…

The purpose of this paper is to give some symmetric identities of higher-order degenerate Euler polynomials derived from the symmetric properties of the multivariate p-adic fermionic integrals on Zp.

In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.

In this letter we investigate some aspects of the noncommutative differential geometry based on derivations of the algebra of endomorphisms of an oriented complex hermitian vector bundle. We relate it, in a natural way, to the geometry of…

We investigate several integer invariants of curves in 3-space. We demonstrate relationships of these invariants to crossing number and to total curvature.

We use spectral theory and algebraic geometry to establish a higher-degree analogue of a Szemer\'edi--Trotter-type theorem over finite fields, with an application to polynomial expansion.

We obtain new recurrence relations, an explicit formula, and convolution identities for higher order geometric polynomials. These relations generalize known results for geometric polynomials, and lead to congruences for higher order…

In this paper, we establish more properties of generalized poly-Euler polynomials with three parameters and we investigate a kind of symmetrized generalization of poly- Euler polynomials. Moreover, we introduce a more general form of multi…

We study an algebra spanned by modified Kostka polynomials. Particular structure coefficients of this algebra are interpreted as traces of some Weyl group actions on the intersection cohomology of comet-shaped quiver varieties.

We study finite dimensional representations of the quantum affine algebra, using geometry of quiver varieties introduced by the author. As an application, we obtain character formulas expressed in terms of intersection cohomologies of…

In this short note, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by L.…

For an arbitrary representation $\rho$ of a complex finite-dimensional Lie algebra, we construct a collection of numbers that we call the Jordan-Kronecker invariants of $\rho$. Among other interesting properties, these numbers provide lower…

We discuss how basic notions of graph theory and associated graph polynomials define questions for algebraic geometry, with an emphasis given to an analysis of the structure of Feynman rules as determined by those graph polynomials as well…

We study identities of Lie superalgebras over a field of characteristic zero. We construct a series of examples of finite-dimensional solvable Lie superalgebras with a non-nilpotent commutator subalgebra for which PI-exponent of codimension…

We introduce the notion of Kravchuk derivations of the polynomial algebra. We prove that any element of the kernel of the derivation gives a polynomial identity satisfied by the Kravchuk polynomials. Also, we prove that any kernel element…