15 citations · 90 across the 32 of their papers we have counts for
4 papers · 1 filter
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…