Assuming data domains are partially ordered, we apply Paredaens' and Bancilhon's Theorem 13, 5] to examine the expressiveness of the relational algebra. We rst extend the relational algebra to the partially ordered re-lational algebra (which we call the PORA) by allowing the ordering predicate v to be used in formulae of the selection operator (). We then show that the PORA expresses exactly th...

If q is an algebraic Lie algebra and Q is an algebraic group with Lie algebra q, then ind q equals the transcendence degree of the field of Q-invariant rational functions on q. If q is reductive, then q and q are isomorphic as q-modules and hence ind q = rk q. It is an important invariant-theoretic problem to study index and, more generally, the coadjoint representation for non-reductive Lie al...

Let A be a unital simple separable C*-algebra satisfying the UCT. Assume that dr(A) < +∞, A is Jiang-Su stable, and K0(A)⊗Q ∼= Q. Then A is an ASH algebra (indeed, A is a rationally AH algebra).

The tensor product of vector and arbitrary representations of the nonstandard q-deformation U ′ q(son) of the universal enveloping algebra U(son) of Lie algebra son is defined. The Clebsch– Gordan coefficients of tensor product of vector and arbitrary classical or nonclassical type representations of q-algebra U ′ q(son) are found in an explicit form. The Wigner–Eckart theorem for vector operat...

Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for t...

We introduce a certain cellular algebra Q(n; r) which is a quotient of the q-Schur algebra S q (n; r). This is naturally equipped with a canonical basis which is compatible with Lusztig's canonical bases for certain modules for the quantized enveloping algebra U (sl n). We describe a diagram calculus for Q(n; r) which makes calculations involving the corresponding canonical bases easy to unders...