We classify all finite dimensional Lie algebras over an algebraically closed field of characteristic 0, whose nonzero elements have abelian centralizers. These algebras are either simple or solvable, where the only simple such Lie algebra is sl2. In the solvable case they are either abelian or a one-dimensional split extension of an abelian Lie algebra.

Split cuts are among the most important and well-understood cuts for general mixed-integer programs. In this paper we consider some recent generalizations of split cuts and compare their relative strength. More precisely, we compare the elementary closures of split, cross, crooked cross and general multi-branch split cuts as well as cuts obtained from multi-row and basic relaxations. We present...

Over a global field any finite number of central simple algebras exponent dividing m is split by common cyclic extension degree m. We show that the same property holds for function fields 2-dimensional excellent schemes over henselian local domain dimension one or two with algebraically closed residue field.

In Secion 1 we describe what is known of the extent to which a separable extension of unital associative rings is a Frobenius extension. A problem of this kind is suggested by asking if three algebraic axioms for finite Jones index subfactors are dependent. In Section 2 the problem in the title is formulated in terms of separable bimodules. In Section 3 we specialize the problem to ring extensi...

Consider a cubic extension K := Q(α), when the minimal polynomial f(x) of α does not totally split in K. The normal closure L := (K) is a sextic extension of Q, with Gal(L/Q) = S3. Now we fix notation and pick one embedding of K as K1, say K1 is fixed by (2, 3) ∈ S3. Here (2, 3) has the explicit description that if I choose one root u1 of f(x), (2, 3) permute the other two conjugate roots of u1...

Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms. This kind of map homomorphism is studied in detail, and generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving. Reconstruction is treated by means of voltage assignments on angles, a natural extension of the common assignments on darts. ...

In a previous paper we derived an expression for the di erentials in the Lyndon-Hochschild-Serre spectral sequence of a split extension G = HoQ of nite groups with coe cients in a eld. Here we apply that result to the case where H and Q are elementary abelian 2-groups and char k = 2. We then work out a special case, in which H has rank 4 and Q has rank 2, from a class of examples constructed by...

Let C and A be categories and P : C → A a functor which is bijective on objects and surjective on arrows; then C is an extension of A. This notion of extension is studied here from the point of view of classifying and synthesizing extensions, by generalizing methods used in studying extensions of groups and semigroups. (Functors which merge objects don’t behave so much like homomorphisms and pr...