Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Lopatin, Artem"'
Publikováno v:
Communications in Mathematics, Volume 33 (2025), Issue 1 (March 27, 2024) cm:13107
In this paper we investigate weak polynomial identities for the Weyl algebra $\mathsf{A}_1$ over an infinite field of arbitrary characteristic. Namely, we describe weak polynomial identities of the minimal degree, which is three, and of degrees 4 and
Externí odkaz:
http://arxiv.org/abs/2402.14799
The set $S(n)$ of all elementary symmetric polynomials in $n$ variables is a minimal generating set for the algebra of symmetric polynomials in $n$ variables, but over a finite field ${\mathbb F}_q$ the set $S(n)$ is not a minimal separating set for
Externí odkaz:
http://arxiv.org/abs/2401.03318
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 $F_q$.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2310.00484
Autor:
Lopatin, Artem
The algebra of ${\rm GL}_n$-invariants of $m$-tuples of $n\times n$ matrices with respect to the action by simultaneous conjugation is a classical topic in case of infinite base field. On the other hand, in case of a finite field generators of polyno
Externí odkaz:
http://arxiv.org/abs/2310.00477
We established two-sided Curto-Herrero conjecture for pairs of matrices, where the first matrix has a simple spectrum. Namely, it is shown that these pairs are separated by ranks of non-commutative polynomials in matrices. Moreover, we provided some
Externí odkaz:
http://arxiv.org/abs/2310.00476
Publikováno v:
Communications in Mathematics, Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024") (March 26, 2024) cm:12323
In this paper we describe the polynomial identities of degree 4 for a certain subspace of the Weyl algebra A_1 over an infinite field of arbitrary characteristic.
Comment: 15 pages. In version 2 proofs were expanded
Comment: 15 pages. In version 2 proofs were expanded
Externí odkaz:
http://arxiv.org/abs/2309.12795
Autor:
Lopatin, Artem, Zubkov, Alexandr N.
Publikováno v:
Alg. Number Th. 18 (2024) 2157-2177
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 and a minimal generating set for G_2-invariants of several copies of the
Externí odkaz:
http://arxiv.org/abs/2209.12620
Autor:
Lopatin, Artem, Zubkov, Alexandr N.
Over an algebraically closed field, we described a minimal set of representatives for G_2-orbits on the set of pairs of octonions. As an application, the case of traceless octonions is considered.
Comment: 16 pages. Version 2 contains essential
Comment: 16 pages. Version 2 contains essential
Externí odkaz:
http://arxiv.org/abs/2208.08122
Publikováno v:
J. Algebra, 595 (2022), 279-296
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 $x,y,$ which satisfy the relation $yx-xy=h$ for some $0\neq h\in \FF[x]$. We generalize th
Externí odkaz:
http://arxiv.org/abs/2111.07013
Publikováno v:
In Linear Algebra and Its Applications 1 July 2024 692:71-83
