15 citations · 90 across the 32 of their papers we have counts for
34 papers
Separating G_2-invariants of several octonions
Artem Lopatin, Alexandr N. Zubkov
We describe separating G_2-invariants of several copies of the algebra of octonions over an algebraically closed field of characteristic two. We also obtain a minimal separating an…
Classification of G_2-orbits for pairs of octonions
Artem Lopatin, Alexandr N. Zubkov
Over an algebraically closed field, we described a minimal set of representatives for G_2-orbits on the set of pairs of octonions.
Identities for a parametric Weyl algebra over a ring
Artem Lopatin, Carlos Arturo Rodriguez Palma
In 2013 Benkart, Lopes and Ondrus introduced and studied in a series of papers the infinite-dimensional unital associative algebra $\A_h$ generated by elements which satisfy…
Separating invariants over finite fields
Gregor Kemper, Artem Lopatin, Fabian Reimers
We determine the minimal number of separating invariants for the invariant ring of a matrix group over the finite field . We show th…
Separating invariants of three nilpotent 3x3 matrices
Felipe Barbosa Cavalcante, Artem Lopatin
The algebra of GL_n-invariants of d-tuple of n x n nilpotent matrices with respect to the action by simultaneous conjugation is generated by the traces of products of nilpotent gen…
Separating invariants for multisymmetric polynomials
Artem Lopatin, Fabian Reimers
This article studies separating invariants for the ring of multisymmetric polynomials in sets of variables over an arbitrary field . We prove that in order to o…