Results 121 to 130 of about 299,272 (139)
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Manin triples for double Lie bialgebroids
Journal of Geometry and Physics19 ...
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Manin Triples of 3-Lie Algebras Induced by Involutive Derivations
Journal of Lie Theory, 2020Summary: Any involutive derivation \(D\) on a 3-Lie algebra \(A\) induces a local cocycle 3-Lie bialgebra (\(A \ltimes_{ad^*} A^*, \Delta)\). We give precise formulas of the 3-Lie algebra \(((A \oplus A^*)^* , \Delta^*)\) and show that the local cocycle 3-Lie bialgebra (\(A \ltimes_{ad^*} A^*, \Delta)\) induced by the involutive derivation \(D\) gives ...
Hou, Shuai, Bai, Ruipu, Sheng, Yunhe
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Manin triples on multiplicative Courant algebroids
Differential Geometry and Its Applications15 ...
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Bialgebras via Manin triples of compatible mock-Lie algebras
Communications in AlgebraKarima Benali
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A New Approach to Jordan D-Bialgebras via Jordan–Manin Triples
Algebra Colloquium, 2022Jordan D-bialgebras were introduced by Zhelyabin. In this paper, we use a new approach to study Jordan D-bialgebras by a new notion of the dual representation of the regular representation of a Jordan algebra. Motivated by the essential connection between Lie bialgebras and Manin triples, we give an explicit proof of the equivalence between Jordan D ...
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Topological Lie Bialgebras, Manin Triples and Their Classification Over g[[x]]
Communications in Mathematical PhysicsLet \((L, [,])\) be a complex Lie algebra. A Lie bialgebra structure on \(L\) is a linear map \(\delta: L \longrightarrow L \otimes L\) making \((L, \delta)\) a Lie coalgebra \[ \mathrm{Alt}_2 \circ \delta = 0, \quad \mathrm{Alt}_3 \circ (\delta \otimes \mathrm{Id}_L) \circ \delta = 0 \] and satisfying the compatibility condition for \(x, y \in L\): \[
Raschid Abedin +3 more
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HOM-ANTICENTER SYMMETRIC ALGEBRAS AND HOM-MOCK LIE ALGEBRAS: MATCHED PAIRS AND MANIN TRIPLES
International Journal of Advanced ResearchThis work develops the hom-algebra theory for anticenter-symmetric algebras by introducing the concept of a hom-anticenter-symmetric algebra. We give their bimodules, dual bimodules and matched pairs. The relation of the bimodules and matched pairs of hom-anticenter-symmetric algebras between those of hom-Mock Lie algebras is discussed.
Gbevewou Damien Houndedji +1 more
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Communications in Contemporary Mathematics
This paper first establishes a bialgebra structure for a noncommutative Novikov algebra, called a noncommutative Novikov bialgebra, which is characterized by matched pairs and Manin triples of noncommutative Novikov algebras. The classical Yang–Baxter type equation, [Formula: see text]-operators, and noncommutative pre-Novikov algebras are introduced ...
Shanghua Zheng +3 more
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This paper first establishes a bialgebra structure for a noncommutative Novikov algebra, called a noncommutative Novikov bialgebra, which is characterized by matched pairs and Manin triples of noncommutative Novikov algebras. The classical Yang–Baxter type equation, [Formula: see text]-operators, and noncommutative pre-Novikov algebras are introduced ...
Shanghua Zheng +3 more
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Admissible hom-Mock Lie Algebras: Dual Representations, Matched Pairs, Manin Triples and Bialgebras
Asian Journal of Mathematics & StatisticsGbêvèwou Damien Houndedji +2 more
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