4 citations · 8 across the 6 of their papers we have counts for
6 papers
Representations of quivers, their generalizations and invariants
A. A. Lopatin, A. N. Zubkov
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between…
The Invariant Ring of Triples of 3x3 Matrices over a Field of Arbitrary Characteristic
A. A. Lopatin
Let R_{n,d} be the ring of invariants of d-tuples of n x n matrices under the simultaneous conjugation action of the general linear group. A minimal generating system and a homogen…
Invariants of quivers under the action of classical groups
A. A. Lopatin
We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups i…
On block partial linearizations of the pfaffian
A. A. Lopatin
Amitsur's formula, which expresses det(A+B) as a polynomial in coefficients of the characteristic polynomial of a matrix, is generalized for partial linearizations of the pfaffian…
Relatively free algebras with the identity x^3=0
A. A. Lopatin
A base of a relatively free associative algebra with the identity x^3=0 over a field of arbitrary characteristic is found. As an application a minimal generating system of the 3x3…
The algebra of invariants of 3x3 matrices over a field of arbitrary characteristic
A. A. Lopatin
The least upper bound on degrees of elements of a minimal system of generators of the algebra of invariants of 3x3 matrices is found, and the nilpotency degree of a relatively free…