The K-groups, the range of trace on K0, and isomorphism classifications are obtained for simple infinite dimensional quotient C*-algebras of the group C*-algebras of six lattice subgroups, corresponding to each of the six non-isomorphic 5-dimensional connected, simply connected, nilpotent Lie groups. Connes’ non-commutative geometry involving cyclic cocycles and the Chern character play a key r...

Canfield and Mason have conjectured that for all subgroups G of the automorphism group of the Boolean lattice Bn (which can be regarded as the symmetric group Sn) the quotient order Bn/G is a symmetric chain order. We provide a straightforward proof of a generalization of a result of K. K. Jordan: namely, Bn/G is an SCO whenever G is generated by powers of disjoint cycles. In addition, the Bool...

We study the asymptotic behaviour of the orbit-counting function and a dynamical Mertens’ theorem for the full G-shift for a finitely-generated torsion-free nilpotent group G. Using bounds for the Möbius function on the lattice of subgroups of finite index and known subgroup growth estimates, we find a single asymptotic of the shape

in this paper we classify fuzzy subgroups of a rank-3 abelian group $g = mathbb{z}_{p^n} + mathbb{z}_p + mathbb{z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. we present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

a lattice boltzmann method is applied to demonstrate the comparison results of simulating natural convection in an open end cavity using different hydrodynamic and thermal boundary conditions. the prandtl number in the present simulation is 0.71, rayleigh numbers are 104,105 and 106 and viscosities are selected 0.02 and 0.05. on-grid bounce-back method with first-order accuracy and non-slip met...

Abstract We give a complete classification of finite subgroups automorphisms K3 surfaces up to deformation. The is in terms Hodge theoretic data associated certain conjugacy classes the orthogonal group lattice. moduli theory surfaces, particular surjectivity period map and strong Torelli theorem allow us interpret this datum geometrically. Our approach computer aided involves Hermitian lattice...

A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion...