A. Baranov

activity

20002020

most citedClassification of the direct limits of involution simple associative algebras and the corresponding dimension groups

21 citations · 43 across the 8 of their papers we have counts for

collaborators

11 papers

math.RT2020

Weight zero in tensor-decomposable irreducible representations of simple algebraic groups

Alexander Baranov, Alexandre Zalesski

Let $G$ be a simple algebraic group in defining characteristic $p > 0$ , and let $V$ be an irreducible $G$ -module which is the tensor product of exactly two non-trivial modules. We ob…

math.RA2018★ 3 cited

Lie structure of associative algebras containing matrix subalgebras

Alexander Baranov

We prove that the Lie commutator subalgebra of the associative algebra containing a matrix subalgebra is perfect.

math.RA2017

Lie algebras graded by the weight system $(Θ_{n}, s l_{n})$

Alexander Baranov, Hogir M. Yaseen

A Lie algebra $L$ is said to be $(Θ_{n}, s l_{n})$ -graded if it contains a simple subalgebra $g$ isomorphic to $s l_{n}$ such that the $g$ -module $L$ decomposes…

math.QA2016

Quantum exceptional group $G_{2}$ and its conjugacy classes

Alexander Baranov, Andrey Mudrov, Vadim Ostapenko

We construct quantization of semisimple conjugacy classes of the exceptional group $G = G_{2}$ along with and by means of their exact representations in highest weight modules of the q…

math.RA2016★ 7 cited

Wedderburn-Malcev decomposition of one-sided ideals of finite dimensional algebras

Alexander Baranov, Andrey Mudrov, Hasan Shlaka

Let $A$ be a finite dimensional associative algebra over a perfect field and let $R$ be the radical of $A$ . We show that for every one-sided ideal $I$ of $A$ there exists a semisim…

math.RA2016

Jordan-Lie inner ideals of finite dimensional associative algebras

Alexander Baranov, Hasan Shlaka

We study Jordan-Lie inner ideals of finite dimensional associative algebras and the corresponding Lie algebras and prove that they admit Levi decompositions. Moreover, we classify…