Rota-Baxter operators on pre-Lie superalgebras

DOI10.1007/s40840-017-0565-xzbMath1435.17019arXiv1512.08043OpenAlexW2776750536WikidataQ59603525 ScholiaQ59603525MaRDI QIDQ2317937

Abdenacer Makhlouf, Sami Mabrouk, El Kadri Abdaoui

Publication date: 13 August 2019

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.08043

zbMATH Keywords

Lie superalgebraRota-Baxter operatorassociative superalgebra\(L\)-dendriform superalgebraspre-Lie superalgebrasuper \(\mathcal{O}\)-operator

Mathematics Subject Classification ID

Graded Lie (super)algebras (17B70) Nonassociative algebras satisfying other identities (17A30) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items

Relative Rota-Baxter operators and symplectic structures on Lie-Yamaguti algebras, Gröbner–Shirshov bases for Lie Ω-algebras and free Rota–Baxter Lie algebras, Hom-Leibniz bialgebras and BiHom-Leibniz dendriform algebras, Hom-prealternative superalgebras, Cohomolgies of Rota-Baxter operators on Lie superalgebras and some classifications on Witt superalgebras, Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman color Hom-algebras, Cohomology and relative Rota-Baxter-Nijenhuis structures on \(\mathsf{LieYRep}\) pairs, Generalized derivations and Rota-Baxter operators of \(n\)-ary Hom-Nambu superalgebras, Rota-Baxter operators on unital algebras, Bihom-pre-Lie superalgebras and related structures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\mathcal O\)-operators on associative algebras and associative Yang-Baxter equations.
• Left-symmetric algebra structures on the \(W\)-algebra \(W(2, 2)\)
• Hom-Lie superalgebras and Hom-Lie admissible superalgebras
• Generalized Lax pairs, the modified classical Yang-Baxter equation, and affine geometry of Lie groups
• An analytic problem whose solution follows from a simple algebraic identity
• New identities in dendriform algebras
• Left-symmetric superalgebraic structures on the super-Virasoro algebras
• Some results on L-dendriform algebras
• A Magnus- and Fer-type formula in dendriform algebras.
• On Lie groups with left-invariant symplectic or Kählerian structures
• Kähler Lie algebras and double extension
• Hopf algebras, renormalization and noncommutative geometry
• Lie-admissible algebras and operads.
• Loday-type algebras and the Rota-Baxter relation
• Classical Yang-Baxter equation and left invariant affine geometry on Lie groups
• On the associative Nijenhuis relation
• Quadri-algebras
• Symplectic double extension of a symplectic Lie group
• Baxter algebras and shuffle products
• Super \(\mathcal{O}\)-operators of Jordan superalgebras and super Jordan Yang-Baxter equations
• Dendriform equations
• The cohomology structure of an associative ring
• Ten mathematics problems I will never solve
• Rota-Baxter algebras and dendriform algebras.
• Left-symmetric algebras, or pre-Lie algebras in geometry and physics
• Baxter operators and endomorphisms on Banach algebras
• On the structure of free Baxter algebras
• Some aspects of Baxter's functional equation
• Rota-Baxter algebras and new combinatorial identities
• CLASSIFICATION OF GRADED LEFT-SYMMETRIC ALGEBRAIC STRUCTURES ON WITT AND VIRASORO ALGEBRAS
• OPERATOR FORMS OF THE CLASSICAL YANG–BAXTER EQUATION IN LIE SUPERALGEBRAS
• Rota-Baxter operators on pre-Lie algebras
• Bijective 1-Cocycles and Classification of 3-Dimensional Left-Symmetric Algebras
• What a Classical r-Matrix Really Is
• ON SOME LEFT-SYMMETRIC SUPERALGEBRAS
• Non-Abelian phase spaces
• Generalizations of the classical Yang-Baxter equation and ${\mathcal O}$O-operators
• A unified algebraic approach to the classical Yang–Baxter equation
• 𝒪-Operators of Loday Algebras and Analogues of the Classical Yang–Baxter Equation
• Rota–Baxter Hom-Lie–Admissible Algebras
• Rota-Baxter operators on $\mathrm{sl(2,\mathbb {C})}$ sl (2,C) and solutions of the classical Yang-Baxter equation
• Complex product structures on Lie algebras
• A FURTHER STUDY ON NON-ABELIAN PHASE SPACES: LEFT-SYMMETRIC ALGEBRAIC APPROACH AND RELATED GEOMETRY
• Domaines bornés homogènes et orbites de groupes de transformations affines
• Symplectic Homogeneous Spaces
• Pre-Poisson algebras