Related papers: Separating invariants for 2x2 matrices
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
The paper deals with the cohomological invariants of smooth and connected linear algebraic groups over an arbitrary field. More precisely, we study degree $2$ invariants with coefficients $\mathbb{Q}/\mathbb{Z}(1)$, that is invariants…
For operators generated by a certain class of infinite band matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying higher order finite difference equations. This…
The minimal log discrepancy is an invariant of singularities that plays an important role in the birational classification of algebraic varieties. Shokurov conjectured that the minimal log discrepancy can always be bounded from above in…
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a)…
Consider the special linear group of degree $2$ over an arbitrary finite field, acting on the full space of $2 \times 2$-matrices by transpose. We explicitly construct a generating set for the corresponding modular matrix invariant ring,…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
In this paper the properties of right invertible row operators, i.e., of 1X2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the…
We investigate the structure of maximal commutative subalgebras of the finite dimensional Grassmann algebra over a field of characteristic different from two.
We characterize the canonical algebras such that for all dimension vectors of homogeneous modules the corresponding module varieties are complete intersections (respectively, normal). We also investigate the sets of common zeros of…
We construct a binary mutation invariant for skew-symmetric integer matrices. The invariant is not an integer congruence invariant for matrices of odd size: we provide examples of congruent such matrices with different values for the…
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…
An explicit form of first order PDE for invariants of binary form are found. By solving the equation a minimal generation set for a ring of invariants and theirs syzygies are calculated in the cases $n\leq 6$ and $n=8.$
Several new invariants for Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.
In this article, we study the ideal generated by $2\times 2$ permanents of a symmetric matrix. We denote this ideal by $P_2(X)$ where $X$ is a symmetric matrix. We compute a Gr\"obner basis, dimension, depth, minimal primes, and a primary…
We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.
Let $A$ be a $2\times 2$ matrix over a finite field and consider the Yang-Baxter matrix equation $XAX=AXA$ with respect to $A$. We use a method of computational ideal theory to explore the geometric structure of the affine variety of all…
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…
We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential…