Related papers: Scalar relative differential invariants
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
We define a two-variable polynomial invariant of finite quandles. In many cases this invariant completely determines the algebraic structure of the quandle up to isomorphism. We use this polynomial to define a family of link invariants…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
We show Laplacian algebras are maximal, and give applications to the Classical Invariant Theory of real orthogonal representations of compact groups, including: The solution of the Inverse Invariant Theory problem for finite groups. An…
The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame…
A quadratic Lie algebra is a Lie algebra endowed with a symmetric, invariant and non degenerate bilinear form; such a bilinear form is called an invariant metric. The aim of this work is to describe the general structure of those central…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
We present in this paper a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces polynomial assignments composed loops analysis to linear loops under certain hypotheses and a…
A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…
We describe the multiplicative invariant algebras of the root lattices of all irreducible root systems under the action of the Weyl group. In each case, a finite system of fundamental invariants is determined and the class group of the…
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…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces,…
Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is…
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
Relative algebroids provide a framework that unifies Lie algebroids with partial differential equations. In this set of notes, we explain how relative algebroids arise from geometric problems, and give an introduction to their structural…