To any manifold equipped with a higher degree closed form, one can associate an L∞-algebra of local observables that generalizes the Poisson algebra of a symplectic manifold. Here, by means of an explicit homotopy equivalence, we interpret this L∞-algebra in terms of infinitesimal autoequivalences of higher prequantum bundles. By truncating the connection data on the prequantum bundle, we produ...

We study the Leibniz $n$-algebra $\textbf{U}_n(\mathfrak{L})$, whose multiplication is defined via bracket of a algebra $\mathfrak{L}$ as $[x_1,\dots,x_n]=[x_1,[\dots, [x_{n-2},[x_{n-1},x_n]]\dots]]$. show that $\textbf{U}_n(\mathfrak{L})$ simple if and only Lie algebra. An analogue Levi's theorem for algebras in $\textbf{U}_n(\textbf{Lb})$ established it proven $n$-kernel any semisimple $\text...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

In this paper, we discuss the properties of some elements in autometrized algebra. We also introduce normal Furthermore, obtain l-algebras among semialgebras satisfying several conditions and discussing its properties. prove that a semialgebra certain is lattice distributive. Finally, establish an equivalent condition between l-algebra representable algebra with conditions. conditions, there ex...

in this paper we consider c0-group of unitary operators on a hilbert c*-module e. in particular we show that if a?l(e) be a c*-algebra including k(e) and ?t a c0-group of *-automorphisms on a, such that there is x?e with =1 and ?t (?x,x) = ?x,x t?r, then there is a c0-group ut of unitaries in l(e) such that ?t(a) = ut a ut*.

based on a complete heyting algebra l, the relations between lfuzzifyingconvergence spaces and l-fuzzifying topological spaces are studied.it is shown that, as a reflective subcategory, the category of l-fuzzifying topologicalspaces could be embedded in the category of l-fuzzifying convergencespaces and the latter is cartesian closed. also the specialization l-preorderof l-fuzzifying convergenc...

Let $fM(X)$ be the  space of  all finite regular Borel measures on $X$. A general measure algebra is a subspace  of$fM(X)$,which is an $L$-space and has a multiplication preserving the probability measures. Let $cLsubseteqfM(X)$ be a general measure algebra on a locallycompact space $X$. In this paper, we investigate the relation between Arensregularity of $cL$ and the topology of $X$. We  find...

Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ∼= U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.

The Birman-Murakami-Wenzl algebra (BMW algebra) of type Dn is shown to be semisimple and free over Z[δ, l]/(m(1 − δ) − (l − l)) of dimension (2n +1)n!!− (2 +1)n!, where n!! = 1 ·3 · · · (2n−1). The Brauer algebra of type Dn is a homomorphic ring image and is also semisimple and free of the same dimension, but over the ring Z[δ]. A rewrite system for the Brauer algebra is used in upper bounding ...

In the theory of dynamical Yang-Baxter equation, with any Hopf algebra H and a certain H-module and H-comodule algebra L (base algebra) one associates a monoidal category. Given an algebra A in that category, one can construct an associative algebra A⋊L, which is a generalization of the ordinary smash product when A is an ordinary H-algebra. We study this ”dynamical smash product” and its modul...