Sentence examples for at algebra from inspiring English sources

LetAbe a simple unital AT algebra of real rank zero such that it has a unique tracial stateτandK1(A) is neither 0 norZ.

Furthermore we construct such anαwith the Rohlin property, which is defined in Kishimoto (Comm. Math. Phys.179(1996), 599 622), in this case the crossed productA×αRis a simple AT algebra of real rank zero.

In this article, we prove that if we further assume that K∗ A) is torsion free, then A is an approximate circle algebra (or an AT algebra), that is, A can be written as the inductive limit ofB1→B2→⋯→Bn→⋯, where Bn="⊕i="1snM{n,i}(C S1)).

As another application of the construction of derivations, we show that ifAis aC*-algebra of the above type andα∈HInn(A) has the Rohlin property and comes fromϕ∈Hom K1(A), R) with dense range as in Kishimoto and Kumjian (preprint), then the crossed productA×αZis again of the same type; in particularA×αZis an AT algebra.

OUR colleagues over at Free Exchange have been mourning the loss of Milton Friedman, reminding us that he was a champion of human freedom as well as a whiz at algebra.

Controls are crucial in science: If every black schoolboy in America knows he's supposed to be good at basketball and bad at algebra, and we have no way to measure schoolboys outside the boundaries of such an expectation, how can we gauge their "natural" endowments?

By applying the classification theory of nuclear C∗-algebras, we use the above result to prove a conjecture of Kishimoto: if A is a unital simple AT-algebra of real rank zero and α∈Aut(A) which is approximately inner and if α satisfies some Rokhlin property, then the crossed product A⋊αZ is again an AT-algebra of real rank zero.

We also point out that there are many simple non-AT algebras generated by irreducible representations of nilpotent groups.

Algebra taught at a public institution is the same as algebra taught at a Catholic institution.

He reports in the Discourse that, when we he was younger, his mathematical studies included some geometrical analysis and algebra (AT VI, 17; CSM I, 119), and he also mentions that he "delighted in mathematics, because of the certainty and self-evidence of its reasonings" (AT VI, 7; CSM I, 114).

Readers of this column may recall that a couple of years ago I figured I'd try tiling, which is sort of like choosing to spend your weekend at an algebra slam.