Related papers: A not so simple local multiplier algebra

Let $(A,\Delta)$ be a locally compact quantum group and $(A_0,\Delta_0)$ a regular multiplier Hopf algebra. We show that if $(A_0,\Delta_0)$ can in some sense be imbedded in $(A,\Delta)$, then $A_0$ will inherit some of the analytic…

The paper is devoted to the study of local derivations and automorphisms of nilpotent Lie algebras. Namely, we proved that nilpotent Lie algebras with indices of nilpotency $3$ and $4$ admit local derivation (local automorphisms) which is…

We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to the case of regular local realizations. A reasonable…

We define and investigate pairings of multiplier Hopf algebras. It is shown that two dually paired regular multiplier Hopf ($*$-)algebras $A$ and $B$ yield a quantum double multiplier Hopf ($*$-)algebra which is again regular. Integrals on…

The Multiplier Hopf Group Coalgebra was introduced by Hegazi in 2002 [7] as a generalization of Hope group caolgebra, introduced by Turaev in 2000 [5], in the non-unital case. We prove that the concepts introduced by A.Van Daele in…

v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition…

A function $q(x)$ is said to be a multiplier from the Sobolev space $H^\al_p(R^n)$ into $H^{-\al}_p(R^n)$ if the operator $Lf(x)=q(x)f(x)$ is a bounded operator from the first space into the second one. Let $M^\al_p$ the the space of such…

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…

We introduce a notion of ternary $F$-manifold algebras which is a generalization of $F$-manifold algebras. We study representation theory of ternary $F$-manifold algebras. In particular, we introduce a notion of dual representation which…

In the present context, we investigate to obtain some more results about $2$-nilpotent multiplier $\mathcal{M}^{(2)}(L)$ of a finite dimensional nilpotent Lie algebra $L$. For instance, we characterize the structure of…

Considered as commutative algebras, cluster algebras can be very unpleasant objects. However, the first author introduced a condition known as "local acyclicity" which implies that cluster algebras behave reasonably. One of the earliest and…

For a locally compact group $G$ and $p \in (1,\infty)$, we define and study the Beurling-Figa-Talamanca-Herz algebras $A_p(G,\omega)$. For $p=2$ and abelian $G$, these are precisely the Beurling algebras on the dual group $\hat{G}$. For $p…

We extend to the context of locally C*-algebras a result of F. Combes [Proc. London Math. Soc. 49(1984), 289-306].

It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…

In the present paper we study local and 2-local derivations of locally finite split simple Lie algebras. Namely, we show that every local and 2-local derivation on such Lie algebra is a derivation.

Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G-representation is non-singular if its cuspidal support is non-singular. We establish a Local Langlands Correspondence…

Let $(A,\Delta)$ be a weak multiplier Hopf algebra. It is a pair of a non-degenerate algebra $A$, with or without identity, and a coproduct $\Delta$ on $A$, satisfying certain properties. The main difference with multiplier Hopf algebras is…

V.A. Rohlin asked in 1949 whether 2-fold mixing implies 3-fold mixing for a stationary process indexed by Z, and the question remains open today. In 1978, F. Ledrappier exhibited a counterexample to the 2-fold mixing implies 3-fold mixing…

Any finite-dimensional Hopf algebra has a left and a right integral. Conversely, Larsen and Sweedler showed that, if a finite-dimensional algebra with identity and a comultiplication with counit has a faithful left integral, it has to be a…

Let M be a paracompact differentiable manifold, A a local algebra and M^{A} a manifold of infinitely near points on M of kind A. We define the notion of A-Poisson manifold on M^{A}. We show that when M is a Poisson manifold, then M^{A} is…