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5 papers
In memory of Igor Dmitrievich Ado
Dietrich Burde, Vsevolod Gubarev
We give a translation from Russian into English of the article "In memory of Igor Dmitrievich Ado" written by A.V. Dorodnov and I.I. Sakhaev and published in Izv.\ Vyssh.\ Uchebn.\…
Decompositions of algebras and post-associative algebra structures
Dietrich Burde, Vsevolod Gubarev
We introduce post-associative algebra structures and study their relationship to post-Lie algebra structures, Rota--Baxter operators and decompositions of associative algebras and…
-polynomial of graph
Vsevolod Gubarev
We define -polynomial of graph which is related to clique, (in)dependence and matching polynomials. The growth rate of partially commutative monoid is equal to the largest root…
Rota--Baxter operators and post-Lie algebra structures on semisimple Lie algebras
Dietrich Burde, Vsevolod Gubarev
Rota--Baxter operators of weight on are in bijective correspondence to post-Lie algebra structures on pairs , where $\mathfrak{n…
Universal enveloping commutative Rota-Baxter algebras of precommutative and postcommutative algebras
Vsevolod Gubarev
Universal enveloping commutative Rota-Baxter algebras of pre- and postcommutative algebras are constructed. We prove that the pair of varieties (commutative Rota-Baxter algebras of…