Let H be a finitely-generated free abelian group and L(H) the graded free Lie algebra on H . There is a natural homomorphism H ⊗ L(H)→ L(H) defined by bracketing, whose kernel is denoted D(H). If H supports a non-singular symplectic form, eg H = H1(Σ), where Σ is a closed orientable surface, with symplectic basis {xi, yi}, then D(H) is, in fact, a Lie algebra. It can be identified with the Lie ...

Kalicki showed in [5] that both of these problems are decidable. Kalicki’s algorithm is obtained by using a fact that only a bounded number of identities has to be verified to decide whether a finite algebra belongs to a finitely generated variety. This approach to the problem turned out to be very inefficient. Bergman and Slutzki presented in [2] an algorithm that solves the universal membersh...

We give a representation theorem for Hilbert algebras by means of ordered sets and characterize the homomorphisms of Hilbert algebras in terms of applications defined between the sets of all irreducible deductive systems of the associated algebras. For this purpose we introduce the notion of order-ideal in a Hilbert algebra and we prove a separation theorem. We also define the concept of semi-h...

In this paper we study the algebra L(Σ) generated by links in the manifold Σ¬[0, 1] where Σ is an oriented surface. This algebra has a filtration and the associated graded algebra L Gr (Σ) is naturally a Poisson algebra. There is a Poisson algebra homomorphism from the algebra ch (Σ) of chord diagrams on Σ to L Gr (Σ). We show that multiplication in L (Σ) provides a geometric way to define a de...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

Abstract Let G be a group and A set equipped with collection of finitary operations. We study cellular automata $$\tau :{A^G} \to {A^G}$$ that preserve the operations induced componentwise from . show τ is an endomorphism if only its local function homomorphism. When entropic (i.e. all are homomorphisms), we establish EndCA( G;A ), consisting such endomorphic automata, isomorphic to direct limi...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Abstract. Let K be any unital commutative Q-algebra and z = (z1, z2, · · · , zn) commutative or noncommutative variables. Let t be a formal central parameter and K[[t]]〈〈z〉〉 the formal power series algebra of z over K[[t]]. In [Z6], for each automorphism Ft(z) = z−Ht(z) of K[[t]]〈〈z〉〉 with Ht=0(z) = 0 and o(H(z)) ≥ 1, a NCS (noncommutative symmetric) system ([Z5]) ΩFt has been constructed. Cons...

1.1. In [1] N. Reshetikhin and the second author introduced new Poisson algebras Wq(g), which are q–deformations of the classical W–algebras. The Poisson algebra Wq(g) is by definition the center of the quantized universal enveloping algebra Uq(ĝ) at the critical level, where g is the Langlands dual Lie algebra to g. It was shown in [1] that the Wakimoto realization of Uq(ĝ ) constructed in [2]...