For an endofunctor H an initial algebra I has, by Lambek’s Lemma, invertible structure map, thus, it can be considered as a coalgebra. We call an H-coalgebra wellfounded if it has a coalgebra homomorphism into I. This is equivalent to the wellfoundedness in Taylor’s “Practical Foundations”, defined by means of an induction principle. And it is also equivalent to the recursivity studied by Capre...

We show that a C *-algebra A is nuclear iff there is a number α < 3 and a constant K such that, for any bounded homomorphism u : A → B(H), there is an isomorphism ξ : H → H satisfying ξ −1 ξ ≤ Ku α and such that ξ −1 u(.)ξ is a *-homomorphism. In other words, an infinite dimensional A is nuclear iff its length (in the sense of our previous work on the Kadison similarity problem) is equal to 2. ...

If X is a topological space we denote by C(X) ® Mn the algebra of continuous functions from X to the algebra Mn of n x n complex matrices. A complete characterization of those topological spaces Y is given (in terms of vector bundles on Y) such that each unital algebrahomomorphism Φ: C(X) Θ Mn —• C(Y) Mkn is of the form a o (Φ' ® idΛ) for some homomorphism Φ': C(X) -+ C(Y) ® Λ/* and some su...

In this paper we introduce a notion of vertex Lie algebra U , in a way a “half” of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U). We show that we may consider U as a subset U ⊂ V(U) which generates V(U) and that the vertex Lie algebra structure on U is induced by the vertex algebra structure on V(U). Moreover, for any vertex ...

A Lie algebra gQ over Q is said to be R-universal if every homomorphism from gQ to gl(n,R) is conjugate to a homomorphism into gl(n,Q) (for every n). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an R-universal Q-form. We also provide a classification of the R-universal Lie algebras that are semisimple.

We study Kuperberg invariants for sutured manifolds in the case of a semidirect product an involutory Hopf superalgebra $H$ with its automorphism group $\text{Aut}(H)$. These are topological balanced 3-manifolds endowed homomorphism fundamental into $\text{Aut}(H)$ and possibly $\text{Spin}^c$ structure homology orientation. show that these computed via form Fox calculus that, if is $\mathbb{N}...

1. I n t r o d u c t i o n 1. Let M be a real-analytic manifold, Vect M the Lie algebra of analytic vector fields on M. We consider a vector field f E Vect M as a differential operator of first order on the algebra of smooth functions C ~ (M) which satisfies the differentiation rule f(W1W2) -" (fw1)W2 + wI(fW2) VWI, W2 E Coo(M). A point z E M will be identified with the corresponding homomorphi...

The algebra Sn of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting, left (but not two-sided) inverses of the canonical generators of the algebra Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of auto...

A class of C*-algebras is described for which the homomorphism from C0(0, 1] to the algebra may be classified by means of the Cuntz semigroup functor. Examples are given of algebras—simple and non-simple—for which this classification fails. It is shown that a suitable suspension of the Cuntz semigroup functor deals successfully with some of these counterexamples.