Related papers: Quasitriangular structures on the 8-dimensional Ka…
The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional Hopf subalgebras. In particular,…
In this paper, we classify eight-dimensional non-solvable Lie algebras that support a symplectic structure. As well as a complete classification is given, up to symplectomorphism, of eight-dimensional symplectic non-solvable Lie algebras.
Let p and q be distinct odd primes and assume k is an algebraically closed field of characteristic zero. We classify all quasitriangular Hopf algebras of dimension pq^2 over k, which are not simple as Hopf algebras. Moreover, we obtained…
The aim of this paper is to give all quasitriangular structures on a class of semisimple Hopf algebras constructed through abelian extensions of $\Bbbk\mathbb{Z}_{2}$ by $\Bbbk^G$ for an abelian group $G$. We first introduce the concept of…
We discuss notions of almost complex, complex and K\"{a}hler structures in the realm of non-commutative geometry and investigate them for a class of finite dimensional spectral triples on the three-point space. We classify all the almost…
We characterize finite-dimensional Lie algebras over an arbitrary field of characteristic zero which admit a non-trivial (quasi-) triangular Lie bialgebra structure.
We give a detailed survey of the theory of quasidiagonal C*-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular we look at what is currently known (and…
We give characterizations of quasitriangular operator algebras along the line of Voiculescu's characterization of quasidiagonal $C^*$-algebras.
We construct quasitoric manifolds of dimension 6 and higher which are not equivariantly homeomorphic to any toric origami manifold. All necessary topological definitions and combinatorial constructions are given and the statement is…
In this paper we study almost complex and almost para-complex Cayley structures on six-dimensional pseudo-Riemannian spheres in the space of purely imaginary octaves of the split Cayley algebra $\mathbf{Ca}'$. It is shown that the Cayley…
Recently we have reformulated the octonions as quasissociative algebras (quasialgebras) living in a symmetric monoidal category. In this note we provide further examples of quasialgebras, namely ones where the nonassociativity is induced by…
We give a degree 8 separable extension having two non-isomorphic Hopf-Galois structures with isomorphic underlying Hopf algebras.
We classify nilpotent Lie algebras with complex structures of weakly non-nilpotent type in real dimension eight, which is the lowest dimension where they arise. Our study, together with previous results on strongly non-nilpotent structures,…
We show that the octonions are a twisting of the group algebra of Z_2 x Z_2 x Z_2 in the quasitensor category of representations of a quasi-Hopf algebra associated to a group 3-cocycle. We consider general quasi-associative algebras of this…
In this article studies questions about the existence of left-invariant K\"{a}hler and semi-para-K\"{a}hler structures on six-dimensional unsolvable Lie groups whose Lie algebras are semidirect products. According to the classification…
Coquasitriangular universal ${\cal R}$ matrices on quantum Lorentz and quantum Poincar\'e groups are classified. The results extend (under certain assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on those objects…
Spectral triples (of compact type) are constructed on arbitrary separable quasidiagonal C*-algebras. On the other hand an example of a spectral triple on a non-quasidiagonal algebra is presented.
In the paper we describe structures of quasitriangular Lie bialgebra on $gl_2(\mathbb C)$ using the classification of Rota-Baxter operators of nonzero weight on $gl_2(\mathbb C)$.
The article presents the structure of the automorphism groups of two types of non-nilpotent Leibniz algebras with a dimension of 3.
One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras. We prove that every contracted QUEA in a certain class is a cochain twist of the…