Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras
نویسندگان
چکیده
منابع مشابه
The Hom-yang-baxter Equation and Hom-lie Algebras
Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by the author in [62]. In this paper, several more classes of solutions of the HYBE are constructed. Some of these solutions of the HYBE are closely related to the quantum enveloping algebra of sl(2), the Jones-Conway polynomial, and Yetter-Drin...
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We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesimal version of the double. We show that there is a natural, but non-obvious way to construct a pre-Lie algebra from an arbitrary infinitesimal bialgebra and a dendriform algebra from a quasitriangular infinitesimal bial...
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Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double shuffle relations for multiple zeta values. The interest in the non-commutative setting arised in connection with the work of Connes and Kreimer on t...
متن کامل2 00 5 Rota - Baxter Algebras , Dendriform Algebras and Poincaré - Birkhoff - Witt Theorem
Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double shuffle relations for multiple zeta values. The interest in the non-commutative setting arose in connection with the work of Connes and Kreimer on th...
متن کاملEnveloping Algebras of Hom-lie Algebras
A Hom-Lie algebra is a triple (L, [−,−], α), where α is a linear self-map, in which the skew-symmetric bracket satisfies an α-twisted variant of the Jacobi identity, called the Hom-Jacobi identity. When α is the identity map, the Hom-Jacobi identity reduces to the usual Jacobi identity, and L is a Lie algebra. Hom-Lie algebras and related algebras were introduced in [1] to construct deformation...
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ژورنال
عنوان ژورنال: Advances in Mathematical Physics
سال: 2020
ISSN: 1687-9120,1687-9139
DOI: 10.1155/2020/9792726