Related papers: On complete system of invariants for the binary fo…

We consider gauge fields associated with a semisimple Malcev algebra. We construct a gauge-invariant Lagrangian and found a solution of modified Yang-Mills equations in seven dimensions.

We introduce the notion of a cellular system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for an algebra to be quasi-hereditary is the existence of a full divisible cellular…

The $3$-element additively idempotent semiring $S_7$ is a nonnitely based algebra of the smallest possible order. In this paper we study the nite basis problem for some additively idempotent semirings that relate to $S_7$. We present a su…

To constitute atoms of a $\sigma$ algebra is not a easy task due to the large number of its elements. However, determining them via generators seems a feasible and simple way since most $\sigma$ algebras are generated by their smaller…

We described a minimal separating set for the algebra of $O(F_q)$-invariant polynomial functions of $m$-tuples of two-dimensional vectors over a finite field $F_q$.

In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when…

This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…

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…

Previously the second author has constructed by cobordism methods, an invariant associated to a finite group $G$. This invariant approximates the number of subgroups of a group, giving in some cases the number of abelian and cyclic…

We construct a normal form for the walled Brauer algebra, together with the reduction algorithm. We apply normal form to calculate the numbers of monomials in generators with minimal length. We further utilize normal form to give explicit…

We obtain a complete classification of minimal simple unitary $W$-algebras.

We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group…

For graded Hilbert spaces $H$ and shift-like commuting tuples $T \in B(H)^n$, we show that each homogeneous joint invariant subspace $M$ of $T$ has finite index and is generated by its wandering subspace. Under suitable conditions on the…

We compute for reflection groups of type $A,B,D,F_4,H_3$ and for dihedral groups a statistic counting the maximal cardinality of a set of elements in the group whose generalized inversions yield the full set of inversions and which are…

We define degree two cohomological invariants for G-Galois algebras over fields of characteristic not 2, and use them to give necessary conditions for the existence of a self--dual normal basis. In some cases, we show that these conditions…

We study local generalized additive decompositions (GADs) of homogeneous polynomials and their associated point schemes through their local inverse systems. We prove that their construction and algebraic properties are independent of the…

We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric construction for their GIT quotients.

This paper reports some advances in the study of the symplectic blob algebra. We find a presentation for this algebra. We find a minimal poset for this as a quasi-hereditary algebra. We discuss how to reduce the number of parameters…

We describe the ring of invariants for the finite orthogonal groups in odd dimension and even characteristic acting on the defining representation. We construct a minimal algebra generating set and describe the relations among the…

It is known that degrees of basic relative invariants of homogeneous open convex cones of rank $r$ are less than or equal to $2^{r-1}$. In this article, we show that there exists a homogeneous cone of rank $r$ one of whose basic relative…