Related papers: Gr\"obner bases for *-algebars and faithful operat…

In this paper we will define analogs of Gr\"obner bases for $R$-subalgebras and their ideals in a polynomial ring $R[x_1,\ldots,x_n]$ where $R$ is a noetherian integral domain with multiplicative identity and in which we can determine ideal…

Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $\pi^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${\cal D} \subset {\cal H}$. Then we…

This note aims to investigate the tensor product of two given Hilbert quasi *-algebras and its properties. The construction proposed in this note turns out to be again a Hilbert quasi *-algebra, thus interesting representability properties…

We prove a finite torsion-free associative conformal algebra to have a finite faithful conformal representation. As a corollary, it is shown that one may join a conformal unit to such an algebra. Some examples are stated to demonstrate that…

In this short note, we construct a variant of the Bohr topos of a C*-algebra which takes into account the topology of the algebra in a finer way and such that this construction is stable under pullback along geometric morphisms. This…

Investigating a recent positive solution of a conjecture of Grunewald and O'Halloran for complex finite dimensional nilpotent Lie algebras, we are in the position to find results of existence and uniqueness for the construction of complex…

We study maximal representations of nonnegative sesquilinear forms in real or complex Hilbert spaces, that are not necessarily closed or even closable. We associate positive self-adjoint operators with such forms, in a sense similar to…

This paper is on $C$ - symmetric creation and annihilation operators, which are constructed on Wick's algebras which fulfil consistency conditions. The essential assumption is that every algebraic action must be constant on equivalence…

We prove a refinement of Ado's theorem for Lie algebras over an algebraically-closed field of characteristic zero. We first define what it means for a Lie algebra $L$ to be approximated with a nilpotent ideal, and we then use such an…

We construct HNN-extensions of Lie di-algebras in the variety of di-algebras and provide a presentation for the replicated HNN-extension of a Lie di-algebras. Then, by applying the method of Gr\"obner-Shirshov bases for replicated algebras,…

In this paper we introduce a working generalization of the theory of Gr\"obner bases for algebras of partial difference polynomials with constant coefficients. One obtains symbolic (formal) computation for systems of linear or non-linear…

We prove that if an amenable operator algebra is nearly contained in a complemented dual operator algebra, then it can be embedded inside this dual operator algebra via a similarity. The proof relies on a B.E. Johnson Theorem on…

We prove an inverse theorem for the Gowers $U^2$-norm for maps $G\to\mathcal M$ from an countable, discrete, amenable group $G$ into a von Neumann algebra $\mathcal M$ equipped with an ultraweakly lower semi-continuous, unitarily invariant…

We prolonge the list of C*-algebras for which all extensions by any stable separable C*-algebra are semi-invertible. In particular, we handle certain amalgamations, both of C*-algebras and of groups. Concerning groups we consider both…

This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…

We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles…

In this work we develop the theory of Gr\"obner bases for modules over the ring of univariate linearized polynomials with coefficients from a finite field.

We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…

We show that any order isomorphism between ordered structures of associative unital JB-subalgebras of JBW algebras is implemented naturally by a Jordan isomorphism. Consequently, JBW algebras are determined by the structure of their…

Following Grothendieck's characterization of Hilbert spaces we consider operator spaces $F$ such that both $F$ and $F^*$ completely embed into the dual of a C*-algebra. Due to Haagerup/Musat's improved version of Pisier/Shlyakhtenko's…