We show that the E-theory of Connes and Higson can be formulated in terms of C∗extensions in a way quite similar to the way in which the KK-theory of Kasparov can. The essential difference is that the role played by split extensions should be taken by asymptotically split extensions. We call an extension of a C∗-algebra A by a stable C∗algebra B asymptotically split if there exists an asymptoti...

We consider generalized exponents of a finite reflection group acting on a real or complex vector space V . These integers are the degrees in which an irreducible representation of the group occurs in the coinvariant algebra. A basis for each isotypic component arises in a natural way from a basis of invariant generalized forms. We investigate twisted reflection representations (V tensor a line...

Following our approach to metric Lie algebras developed in a previous paper we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric space M to a t...

Many important quantum algebras such as quantum symplectic space, quantum Euclidean space, quantummatrices, q-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras U(L+) of even Lie color algebras are also semi-commutative. In this paper, we generalize work of Montgomery and examine the X-inner automorphisms of such algebras. The t...

Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let gI be the corresponding semi-simple subalgebra of g. Denote by WI the Weyl group of gI and let w◦ and w I ◦ be the longest elements of W and WI , respectively. In this paper we show that the answer to Kostant’s problem, i.e. whether the universal enveloping algebra surjects on...

Let M be a von Neumann algebra (not necessarily semi-finite). We provide a generalization of the classical Kadec-Pe lczynski subsequence decomposition of bounded sequences in L[0, 1] to the case of the Haagerup L-spaces (1 ≤ p < ∞). In particular, we prove that if (φn)n is a bounded sequence in the predual M∗ of M, then there exist a subsequence (φnk)k of (φn)n, a decomposition φnk = yk + zk su...

Let X be a smooth projective surface, Coh(X) the abelian category of coherent sheaves on X, and D(X) the bounded derived category of coherent sheaves on X. We study the Bridgeland stability conditions on D(X) and see that for some stability conditions on D(X) the moduli spaces of (semi)stable objects in D(X) coincide with the moduli spaces of (semi)stable coherent sheaves, while for some other ...

it is shown that every  almost linear bijection $h : arightarrow b$ of a unital $c^*$-algebra $a$ onto a unital$c^*$-algebra $b$ is a $c^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in a$, all $y in a$, and all $nin mathbb z$, andthat almost linear continuous bijection $h : a rightarrow b$ of aunital $c^*$-algebra $a$ of real rank zero onto a unital$c^*$-algebra...

A solution method for solving Markov chains for a class of stochastic process algebra terms is presented. The solution technique is based on a reformulation of the underlying continuous-time Markov chain (CTMC) in terms of semi-Markov processes. For the reformulation only local information about the processes running in parallel is needed, and it is therefore never necessary to generate the com...

T he mathematical work of Irving Kaplansky, who passed away in June 2006, is largely devoted to algebra. Irving’s base camp in mathematics was undeniably algebra. But all of us in functional analysis classify Irving as a mathematician—someone capable of working in and drawing inspiration from all areas of mathematics. He is considered by all my coworkers in operator algebra theory to be one of ...