Decompositions of algebras and post-associative algebra structures
| Autor: | Vsevolod Gubarev, Dietrich Burde |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics 17B20 17D25 Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Mathematics - Rings and Algebras 010103 numerical & computational mathematics 01 natural sciences Algebra Rings and Algebras (math.RA) Lie algebra Associative algebra FOS: Mathematics Computer Science::General Literature 0101 mathematics Algebra over a field Mathematics::Representation Theory Associative property Mathematics |
| Zdroj: | International Journal of Algebra and Computation. 30:451-466 |
| ISSN: | 1793-6500 0218-1967 |
| DOI: | 10.1142/s0218196720500071 |
| Popis: | We introduce post-associative algebra structures and study their relationship to post-Lie algebra structures, Rota–Baxter operators and decompositions of associative algebras and Lie algebras. We show several results on the existence of such structures. In particular, we prove that there exists no post-Lie algebra structure on a pair [Formula: see text], where [Formula: see text] is a simple Lie algebra and [Formula: see text] is a reductive Lie algebra, which is not isomorphic to [Formula: see text]. We also show that there is no post-associative algebra structure on a pair [Formula: see text] arising from a Rota–Baxter operator of [Formula: see text], where [Formula: see text] is a semisimple associative algebra and [Formula: see text] is not semisimple. The proofs use results on Rota–Baxter operators and decompositions of algebras. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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