A note on triangular derivations of

For a field of characteristic zero, and for each integer , we construct a triangular derivation of whose ring of constants, though finitely generated over , cannot be generated by fewer than elements.

     

Characterization of derivations on B(X) by local actions

Let A be a unital algebra and M be a unital A-bimodule. A linear map δ : A →M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ? B + A ? δ(B) =δ(A ? B) for any A, B ∈ A with A ? B = P, here A ? B = AB + BA is the usual Jordan product. In this article, we show that if A = Alg N is a Hilbert space nest algebra and M = B(H), or A = M = B(X), then, a linear map δ : A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B(X) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.     

Infinitesimal Generators of C *-Algebras

We develop the method introduced previously, to construct infinitesimal generators on locally compact group C ^*-algebras and on tensor product of C ^*-algebras. It is shown in particular that there is a C ^* -algebra A such that the C ^*-tensor product of A and an arbitrary C ^*-algebra B can have a non-approximately inner strongly one parameter group of ^*-automorphisms.     

Domains of infinitesimal generators of automorphism flows

We present a systematic characterization of the domain of a generator of a one parameter group on certain C∗-subalgebras of via finite-dimensional estimates. Our approach yields an example of a densely defined closed symmetric derivation on a C∗-subalgebras of whose domain is not closed with respect to the C¹-functional calculus. This completes and complements the earlier example of McIntosh (J. Funct. Anal. 30 (1977) 264). Our methods are partly based on the theory of adjoint C₀-semigroups.     

Some Simple Derivations of k[x,y]

It is shown that the derivation y ^r ? _x  + (xy ^s  + g)? _y , where 0 ≤ r < s are integers, is a simple derivation of k[x, y], the polynomial ring in two variables over a field k of characteristic zero.     

Dérivations des Algèbres de Weyl Quantiques Multiparamétrées et de Certaines de leurs Localisations Simples

ABSTRACT

On calcule une base explicite de l'espace des dérivations modulo les dérivations intérieures des algèbres de Weyl quantiques et de certaines de leurs localisations simples. On applique les résultats obtenus à des questions de séparation à équivalence de Morita près de ces algèbres.

We compute an explicit basis of the space of derivations modulo inner derivations for quantum Weyl algebras and some of their simple localizations. We apply these results to separate these algebras up to Morita equivalence.

     

ON THE ZEROS OF POLYNOMIALS OVER QUATERNIONS

ABSTRACT

We review and expand some results on the number of zeros of polynomials over Hamilton's quaternions, with particular emphasis on those polynomials with coefficients in a degree two subfield.     

ON SECONDARY MODULES OVER PULLBACK RINGS

Abstract

In this paper we describe the derivations of orthosymplectic Lie superalgebras over a superring. In particular, we derive sufficient conditions under which the derivations can be expressed as a semidirect product of inner and outer derivations. We then present some examples for which these conditions hold.