Related papers: Hopf Structure in Nambu-Lie n-Algebras
The aim of this paper is to investigate the cohomologies for ternary algebras of associative type. We study in particular the cases of partially associative ternary algebras and weak totally associative ternary algebras. Also, we consider…
The set of primitive elements of a Hopf algebra in the braided category of group graded vector spaces (with a commutative group) carry the structure of a generalized Lie algebra. In particular the graded derivations of an associative…
The paper studies the structure of restricted hom-Lie algebras. More specifically speaking, we first give the equivalent definition of restricted hom-Lie algebras. Second, we obtain some properties of $p$-mappings and restrictable hom-Lie…
In this paper, we discuss the representations of $n$-ary multiplicative Hom-Nambu-Lie superalgebras as a generalization of the notion of representations for $n$-ary multiplicative Hom-Nambu-Lie algebras. We also give the cohomology of an…
We give a degree 8 separable extension having two non-isomorphic Hopf-Galois structures with isomorphic underlying Hopf algebras.
We describe a new method of quantization of Lie bialgebras, based on a construction of Hopf algebras out of a cocommutative coalgebra and a braided comonoidal functor.
Building on the work of Nenciu we provide examples of non-factorizable ribbon Hopf algebras, and introduce a stronger notion of non-factorizability. These algebras are designed to provide invariants of $4$-dimensional $2$-handlebodies up to…
Let p be a prime, and k be a field of characteristic p. We investigate the algebra structure and the structure of the cohomology ring for the connected Hopf algebras of dimension p^3, which appear in the classification obtained in [V.C.…
Every multiplicative Hom-Malcev algebra has a natural multiplicative Hom-Lie triple system structure. Moreover, there is a natural Hom-Bol algebra structure on every multiplicative Hom-Malcev algebra and on every multiplicative right (or…
Let $\mathbb{K}$ be the set of hybrid numbers. This paper is to look for all the weak Hopf structures on $\mathbb{K}$. Once $\mathbb{K}$ is endowed with a structure of a weak Hopf algebra, we shall compute the source algebra and target…
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive…
We study the Hopf algebra of double posets and two of its Hopf subalgebras, the Hopf algebras of plane posets and of posets "without N". We prove that they are free, cofree, self-dual, and we give an explicit Hopf pairing on these Hopf…
The notion of inner linear Hopf algebra is a generalization of the notion of discrete linear group. In this paper, we prove two general results that enable us to enlarge the class of Hopf algebras that are known to be inner linear: the…
We investigate several Hopf algebras of diagrams related to Quantum Field Theory of Partitions and whose product comes from the Hopf algebras WSym or WQSym respectively built on integer set partitions and set compositions. Bases of these…
A ternary Nambu-Poisson algebra (which we call a Nambu-Poisson algebra in the paper) is the underlying algebraic structure of Nambu-Poisson manifolds of order $3$ that appeared in the generalized Hamiltonian mechanics. First, we consider…
In this paper, first we introduce the notion of a nonabelian embedding tensor on the 3-Lie algebra. Then, we introduce the notion of a 3-Leibniz-Lie algebra, which is the underlying algebraic structure of a nonabelian embedding tensor on…
We study the Hopf algebra structure of Lusztig's quantum groups. First we show that the zero part is the tensor product of the group algebra of a finite abelian group with the enveloping algebra of an abelian Lie algebra. Second we build…
We derive necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type. This construction generalizes the notion of Hopf-Ore extension, called a generalized Hopf-Ore…
We demonstrate that the fundamental algebraic structure underlying the Connes-Kreimer Hopf algebra -- the insertion pre-Lie structure on graphs -- corresponds directly to the canonical pre-Lie structure of polynomial vector fields. Using…
Bialgebras and Hopf (bi)modules are typical algebraic structures with several interacting operations. Their structural and homological study is therefore quite involved. We develop the machinery of braided systems, tailored for handling…