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Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras
This paper extends the well-known fact that a Rota-Baxter operator of weight 0 on a Lie algebra induces a pre-Lie algebra, to the level of...
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Extending Structures for Gel’fand-Dorfman Bialgebras
Gel’fand-Dorfman bialgebra, which is both a Lie algebra and a Novikov algebra with some compatibility condition, appeared in the study of Hamiltonian...
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Construction and Characterization of n-Ary Hom-Bialgebras and n-Ary Infinitesimal Hom-Bialgebras
Constructions of n-ary bialgebras and n-ary infinitesimal bialgebras of associative type and their hom-analogs, generalizing the hom-bialgebras and...
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Nearly Associative and Nearly Hom-Associative Algebras and Bialgebras
BasicDassoundo, Mafoya Landry Silvestrov, Sergei definitions and properties of nearly associative algebras are described. Nearly associative algebras...
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Lie Bialgebra Structure of Derivation Lie Algebra over Quantum Torus
In this paper, all Lie bialgebra structures on the derivation Lie algebra W over a rank d ≥ 3 quantum torus associated to q are considered, where q ...
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Hom-Leibniz bialgebras and BiHom-Leibniz dendriform algebras
A notion of a Hom-Leibniz bialgebra is introduced and it is shown that matched pairs of Hom-Leibniz algebras, Manin triples of Hom-Leibniz algebras...
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A new approach to antisymmetric infinitesimal bialgebras
We present a notion of an anti-covariant bialgebra extending the anti-symmetric infinitesimal bialgebra and also provide some equivalent...
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Hom-Lie Algebras with Derivations
In this paper, we first introduce the notion of an HLieDer triple, which includes a Hom-Lie algebra and a derivation. We define a cohomology theory...
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(Hom-)(co)associative Ternary (Co)algebras and Infinitesimal Ternary (Hom-)bialgebras
The partially and totally (co)associative ternary (co) algebras, and infinitesimal bialgebras are constructed and discussed. Their trimodules and...
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3-Bihom-ρ-Lie Algebras, 3-Pre-Bihom-ρ-Lie Algebras
The purpose is to introduce the notions of 3-Bihom- ρ -Lie algebras and 3-pre-Bihom- ρ -Lie algebras. The authors describe their constructions and...
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Weighted infinitesimal unitary bialgebras of rooted forests, symmetric cocycles and pre-Lie algebras
The concept of weighted infinitesimal unitary bialgebra is an algebraic meaning of the nonhomogenous associative Yang–Baxter equation. In this paper,...
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DIFFERENTIAL GRADED LIE GROUPS AND THEIR DIFFERENTIAL GRADED LIE ALGEBRAS
In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to differential graded Lie groups (DGLG). We first...
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Lie Theory for Quasi-Shuffle Bialgebras
Many features of classical Lie theory generalize to the broader context of algebras over Hopf operads. However, this idea remains largely to be...
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Lie Bialgebroid of Pseudo-differential Operators
We associate a Lie bialgebroid structure to the algebra of formal Pseudo-differential operators, as the classical limit of a quantum groupoid. As a...
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Cohomology and Deformations of Compatible Lie Triple Systems
In this paper, we first introduce the notions of a compatible Lie triple system and its representation. We construct a bidifferential graded Lie...
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On pseudo-Hermitian quadratic nilpotent lie algebras
We study nilpotent Lie algebras endowed with a complex structure and a quadratic structure which is pseudo-Hermitian for the given complex structure....
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Maurer-Cartan characterizations and cohomologies of compatible Lie algebras
In this paper, we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie algebras. Explicitly, we first introduce the...
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On \((\lambda ,\mu ,\gamma )\) -Derivations of BiHom-Lie Algebras
In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the...
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Post-groups, (Lie-)Butcher groups and the Yang–Baxter equation
The notions of a post-group and a pre-group are introduced as a unification and enrichment of several group structures appearing in diverse areas...