This is the second of three lectures on introduction to vertex operator algebras. In this lecture, we shall continue Professor Dong’s lecture to present more fundamental properties of vertex operator algebras. From the mathematical point of view, a vertex operator algebra formally resembles a Lie algebra because the Jacobi identity is used as one of the main axioms. For the Lie algebra aspect o...

Deuber’s Theorem says that, given any m, p, c, r in N, there exist n, q, μ in N such that whenever an (n, q, c)-set is r-coloured, there is a monochrome (m, p, c)-set. This theorem has been used in conjunction with the algebraic structure of the StoneČech compactification βN of N to derive several strengthenings of itself. We present here an algebraic proof of the main results in βN and derive ...

The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra Uq(g), and the structure of a co-module algebra over the quantum group Gq associated with Uq(g). These two algebraic structures are dual to each other via the duality between Gq and Uq(g).

We prove that if G is an algebraic D-group (in the sense of Buium [B]) over a differentially closed field (K, ∂) of characteristic 0, then the first order structure consisting of G together with the algebraic D-subvarieties of G,G × G, . . ., has quantifier-elimination. In other words, the projection on Gn of a D-constructible subset of Gn+1 is Dconstructible. Among the consequences is that any...

We construct a universal and even logically fully abstract realizability model for the sequential functional programming language of call-by-name FPC. This model is defined within the category of modest sets over the total combinatory algebra L of observational equivalence classes of closed terms of the untyped programming language λ+Error. This language is untyped lazy call-by-name lambda-calc...

We prove that given any n-pointed prestable curve C of genus g with linearly reductive automorphism group Aut(C), there exists an Aut(C)equivariant miniversal deformation of C over an affine variety W . In other words, we prove that the algebraic stack Mg,n parametrizing n-pointed prestable curves of genus g has an étale neighborhood of [C] isomorphic to the quotient stack [W/Aut(C)].

Rational terms (possibly innnite terms with nitely many subterms) can be represented in a nite way via-terms, that is, terms over a signature extended with self-instantiation operators. For example, f ! = f(f(f(: : :))) can be represented as x:f(x) (or also as x:f(f(x)), f(x:f(x)),. . .). Now, if we reduce a-term t to s via a rewriting rule using standard notions of the theory of Term Rewriting...

ABSTRACT In this article we introduce a universal C (∗)-algebras associated to certain simplicial flag complexes. We denote it by [Formula: see text]it is a subalgebra of the noncommutative n-sphere which introduced by J.Cuntz. We present a technical lemma to determine the quotient of the skeleton filtration of a general universal C (∗)-algebra associated to a simplicial flag complex. We examin...

We introduce and study continuous fields of JB-algebras (which are real non-associate analogues of C*-algebras). In particular, we show that for the universal enveloping C*-algebra C∗ u (B) for the JB-algebra B defined by a continuous field of JB-algebras At, t ∈ T, on a locally compact space T there exists a decomposition of C∗ u (B) into a continuous field of C*-algebras C∗ u (At), t ∈ T, on ...