Simple finite-dimensional double algebras Full article
| Journal |
Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X |
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| Output data | Year: 2018, Volume: 500, Pages: 425-438 Pages count : 14 DOI: 10.1016/j.jalgebra.2017.04.020 | ||
| Tags | Averaging operator; Double Lie algebra; Rota–Baxter operator | ||
| Authors |
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| Affiliations |
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Abstract:
A double algebra is a linear space V equipped with linear
map V ⊗ V → V ⊗ V . Additional conditions on this map
lead to the notions of Lie and associative double algebras.
We prove that simple finite-dimensional Lie double algebras
do not exist over an arbitrary field, and all simple finite-
dimensional associative double algebras over an algebraically
closed field are trivial. Over an arbitrary field, every simple
finite-dimensional associative double algebra is commutative.
A double algebra structure on a finite-dimensional space V
is naturally described by a linear operator R on the algebra
End V of linear transformations of V . Double Lie algebras
correspond in this sense to skew-symmetric Rota–Baxter
operators, double associative algebra structures – to (left)
averaging operators.
Cite:
Goncharov M.E.
, Kolesnikov P.S.
Simple finite-dimensional double algebras
Journal of Algebra. 2018. V.500. P.425-438. DOI: 10.1016/j.jalgebra.2017.04.020 WOS Scopus OpenAlex
Simple finite-dimensional double algebras
Journal of Algebra. 2018. V.500. P.425-438. DOI: 10.1016/j.jalgebra.2017.04.020 WOS Scopus OpenAlex
Dates:
| Submitted: | Sep 13, 2016 |
| Published online: | May 3, 2017 |
Identifiers:
| Web of science: | WOS:000427548000021 |
| Scopus: | 2-s2.0-85044260493 |
| OpenAlex: | W2554412622 |