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pro vyhledávání: '"Koshlukov, Plamen"'
Let $K$ be a field of characteristic zero and let $\mathfrak{sl}_2 (K)$ be the 3-dimensional simple Lie algebra over $K$. In this paper we describe a finite basis for the $\mathbb{Z}_2$-graded identities of the adjoint representation of $\mathfrak{sl
Externí odkaz:
http://arxiv.org/abs/2411.00811
Let $A=A_1\oplus\cdots\oplus A_r$ be a decomposition of the algebra $A$ as a direct sum of vector subspaces. If for every choice of the indices $1\le i_j\le r$ there exist $a_{i_j}\in A_{i_j}$ such that the product $a_{i_1}\cdots a_{i_n}\ne 0$, and f
Externí odkaz:
http://arxiv.org/abs/2410.13600
Autor:
Códamo, Ramon, Koshlukov, Plamen
In this paper we study algebras acted on by a finite group $G$ and the corresponding $G$-identities. Let $M_2( \mathbb{C})$ be the $2\times 2$ matrix algebra over the field of complex numbers $ \mathbb{C}$ and let $sl_2( \mathbb{C})$ be the Lie algeb
Externí odkaz:
http://arxiv.org/abs/2402.13986
Autor:
Códamo, Ramon, Koshlukov, Plamen
Let $D$ be a Noetherian infinite integral domain, denote by $M_2(D)$ and by $sl_2(D)$ the $2\times 2$ matrix algebra and the Lie algebra of the traceless matrices in $M_2(D)$, respectively. In this paper we study the natural grading by the cyclic gro
Externí odkaz:
http://arxiv.org/abs/2402.13982
Autor:
Fagundes, Pedro, Koshlukov, Plamen
Let $A=B+C$ be an associative algebra graded by a group $G$, which is a sum of two homogeneous subalgebras $B$ and $C$. We prove that if $B$ is an ideal of $A$, and both $B$ and $C$ satisfy graded polynomial identities, then the same happens for the
Externí odkaz:
http://arxiv.org/abs/2307.06112
Let $UT_n(F)$ be the algebra of the $n\times n$ upper triangular matrices and denote $UT_n(F)^{(-)}$ the Lie algebra on the vector space of $UT_n(F)$ with respect to the usual bracket (commutator), over an infinite field $F$. In this paper, we give a
Externí odkaz:
http://arxiv.org/abs/2208.08550
Autor:
Fagundes, Pedro, Koshlukov, Plamen
In this paper we study the images of multilinear graded polynomials on the graded algebra of upper triangular matrices UT_n. For positive integers q \leq n, we classify these images on UT_n endowed with a particular elementary Z_q-grading. As a conse
Externí odkaz:
http://arxiv.org/abs/2205.10698
Autor:
Códamo, Ramon, Koshlukov, Plamen
Publikováno v:
In Linear Algebra and Its Applications 1 October 2024 698:326-343
Publikováno v:
In Journal of Algebra 15 February 2025 664 Part A:756-779
Autor:
Fidelis, Claudemir, Koshlukov, Plamen
Let $K$ be any field of characteristic two and let $U_1$ and $W_1$ be the Lie algebras of the derivations of the algebra of Laurent polynomials $K[t,t^{-1}]$ and of the polynomial ring $K[t]$, respectively. The algebras $U_1$ and $W_1$ are equipped w
Externí odkaz:
http://arxiv.org/abs/2112.15048