Related papers: On minimal generating systems for matrix O(3)-inva…

We display a new family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring over a field of characteristic zero. These primes are obtained as the kernel of a quasi-monomial algebra…

We obtain tight bounds for the minimal number of generators of an ideal with bounded-degree generators in a polynomial ring $K[X_1,\dots,X_n],$ as well as a sharp quantification of the maximum possible size of a minimal generating set of…

2$\leftrightarrow$3 symmetry is realized by the breaking from alterating group of degree 4 ($A4$) symmetry. $A4$ explains why the generation number is three. However the mass matrices are realized in the form of the breaking to…

We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…

The tridiagonal algebra is defined by two generators and two relations, called the tridiagonal relations. Special cases of the tridiagonal algebra include the $q$-Onsager algebra, the positive part of the $q$-deformed enveloping algebra…

For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras -- special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central.…

This paper finds for all orthogonal algebras (i.e. the B and D series) all modular invariant 1-loop partition functions at levels 1,2,3. Previously, only those at level 1 were classified. An extraordinary number of exceptionals appear at…

We consider finite dimensional representations of the dihedral group $D_{2p}$ over an algebraically closed field of characteristic two where $p$ is an odd integer and study the degrees of generating and separating polynomials in the…

Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…

The orbits in $\Gamma_{\infty}(3) \backslash \Gamma(3)$ are in bijection with sets of invariants satisfying certain relations. We explain how wedge product matrices give an alternative definition of the invariants of matrix orbits. This new…

The ring of invariant polynomials ${\mathbb C}[V]^G$ over a given finite dimensional representation space $V$ of a complex reductive group $G$ is known, by a famous theorem of Hilbert, to be finitely generated. The general proof being…

Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously include the subsets of diagonalizable and nilpotent matrices. In…

We prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language. We also study the cohomology of the…

The single defining relation of the algebra of $SL_3\times SL_3$-invariants of triples of $3\times 3$ matrices is explicitly computed. Connections to some other prominent algebras of invariants are pointed out.

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…

The background of this paper is the following: search of the minimal systems of generators for this class of group which still was not founded also problem of representation for this class of group, exploration of systems of generators for…

We prove that many of the results of the LMMP hold for $3$-folds over fields of characteristic $p>5$ which are not necessarily perfect. In particular, the existence of flips, the cone theorem, the contraction theorem for birational extremal…

We obtain an asymptotic upper bound for the smallest number of generators for a finite direct sum of matrix algebras with entries in a finite field. This produces an upper bound for a similar quantity for integer matrix rings. We also…

Operators acting on the discrete random chaos yield signed multiplicative systems, extending the notion of spin matrices and quaternions. We investigate signed groups through the associated sign matrices, focusing on generators and their…

We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…