In ‎this ‎paper, ‎we ‎study ‎the ‎relation ‎between ‎the ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎with ‎the ‎lattice theory. ‎We ‎introduce ‎the ‎concepts ‎of ‎the ‎lattice ‎of ‎soft ‎sets, ‎full ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎and next, we ‎verify ‎some ‎properties ‎of ‎them. We ‎prove ‎that ‎the ‎lattice ‎of ‎the ‎soft ‎sets ‎on ‎a fixed parameter set is isomorphic to the power set of a ...

We introduce the growth rank of a C∗-algebra — a (N∪ {∞})-valued invariant whose minimal instance is equivalent to the condition that an algebra absorbs the Jiang-Su algebra Z tensorially — and prove that its range is exhausted by simple, nuclear C∗-algebras. As consequences we obtain a well developed theory of dimension growth for approximately homogeneous (AH) C∗-algebras, establish the exist...

We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. show that any action is equivariantly KK-equivalent an a simple, purely infinite C*-algebra. conjecture Izumi equivalent equivalence between cocycle conjugacy and KK-equivalence for torsion-free amenable groups Kirchberg algebras. Let G be cyclic prime order. describe its KK-equivalence, based previous...

In [2], Bost and Connes studied a particular Hecke C-algebra CQ arising in number theory. The algebra CQ can be realised as a semigroup crossed product C (Q/Z)⋊αN ∗ by an endomorphic action α of the multiplicative semigroup N on the group Calgebra C(Q/Z) [7], and this realisation has provided useful insight into the analysis of CQ [5, 13]. Since individual elements of Q/Z and N ∗ involve only f...

In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension 10 over any field. It is known that symplectic alternating algebras over GF(3) correspond to a special rich class C of 2-Engel 3-groups of exponent 27 and under this correspondance we will see that the nilpotent algebras corre...

1. Summary. My prior and current research is primarily concerned with the internal structure, representation theory, and \noncommutative aane geometry" of certain classes of associative algebras. The examples directly involved arise from algebraic quantum groups, nite dimensional Lie superalgebras, and polycyclic-by-nite-groups; in particular, Hopf (super)algebras play an essential part. My foc...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...