Related papers: Biquasigroups linear over a group

We show that quasiconformal maps on many Carnot groups must be biLipschitz. In particular, this is the case for 2-step Carnot groups with reducible first layer. These results have implications for the rigidity of quasiisometries between…

We study linear actions of finite groups in small dimensions, up to equivariant birationality.

We prove the main result that a groupoid of order n is an idempotent k-translatable quasigroup if and only if its multiplication is given by x.y = (ax+by)(mod n), where a+b = 1(mod n), a+bk = 0(mod n) and (k,n)= 1. We describe the structure…

We find all the possible torsion groups of $\Q$-curves over quadratic fields and determine which groups appear finitely and which appear infinitely often.

For a certain class of Lie bialgebras $(A,A^*)$ the corresponding quantum universal enveloping algebras $U_q(A)$ are prooved to be equivalent to quantum groups Fun$_q(F^*)$, $F^*$ being the factor group for the dual group $G^*$. This…

We present a bicovariant differential calculus on the quantum Poincare group in two dimensions. Gravity theories on quantum groups are discussed.

We study {\em right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures} on a Lie group $G$ and introduce their infinitesimal counterpart, the so-called {\em r-qn structures} on the corresponding Lie algebra $\mathfrak g$.…

A brief review of the construction and classifiaction of the bicovariant differential calculi on quantum groups is given.

The general expression for the bicovariant bracket for odd generators of the external algebra on a Poisson-Lie group is given. It is shown that the graded Poisson-Lie structures derived before for $GL(N)$ and $SL(N)$ are the special cases…

Beginning with a skew-symmetric matrix, we define a certain Poisson--Lie group. Its Poisson bracket can be viewed as a cocycle perturbation of the linear (or "Lie-Poisson") Poisson bracket. By analyzing this Poisson structure, we gather…

We compute the group of Morita self-equivalences (the Picard group) of a Poisson structure on an orientable surface, under the assumption that the degeneracies of the Poisson tensor are linear. The answer involves mapping class groups of…

We provide an equivariant extension of the bivariant Cuntz semigroup introduced in previous work for the case of compact group actions over C*-algebras. Its functoriality properties are explored and some well-known classification results…

We consider the dual space of linear groups over Dynkinian and Euclidean algebras, i.e. finite dimensional algebras derived equivalent to the path algebra of Dynkin or Euclidean quiver. We prove that this space contains an open dense subset…

We show that $L_{\infty}$-algebroids, understood in terms of Q-manifolds can be described in terms of certain higher Schouten and Poisson structures on graded (super)manifolds. This generalises known constructions for Lie (super)algebras…

We describe the classification of ranked definably quasi-Frobenius groups of odd type : dihedral configurations are isomorphic to PGL(2, K) for K an algebraically closed field of characteristic other than two; Frobenius groups are spilt and…

In this paper, the theory to construct quantum lines for general dual quasi-bialgebras is developed followed by some specific examples where the dual quasi-bialgebras are pointed with cyclic group of points.

All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie-Poisson structures on Galilei group are found.

We recall the notion of Hopf quasigroups introduced previously. We construct a bicrossproduct Hopf quasigroup $kM\bicross k(G)$ from every group $X$ with a finite subgroup $G\subset X$ and IP quasigroup transversal $M\subset X$ subject to…

In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers…

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.