Operator Systems from Discrete Groups

Operator Growth Functions of Discrete Groups

A generalizationof the growth functions of nitelygeneratedgroups is introduced, namely the growth functionswith operatorcoeecients g2G gz jgj. The questions of rationality and convergence of such series are discussed. The operator growth functions of surface groups are explicitly computed. The operator geodesic growth functions are also studied.

Dirac-Connes Operator on Discrete Abelian Groups and Lattices

A kind of Dirac-Connes operator defined in the framework of Connes’ NCG is introduced on discrete abelian groups; it satisfies a Junk-free condition, and bridges the NCG composed by Dimakis, MüllerHoissen and Sitarz and the NCG of Connes. Then we apply this operator to d-dimensional lattices. [email protected] [email protected]

Paragrassmann Integral, Discrete Systems and Quantum Groups

This report is based on review paper [1]. Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the Z p+1 Potts model on a chain. Finite dimensional paragrassmann representations for GL q (2) are constructed. Generalizations of grassmann al...

Discrete Nonholonomic LL Systems on Lie Groups

This papers studies discrete nonholonomic mechanical systems whose configuration space is a Lie group G Assuming that the discrete Lagrangian and constraints are left-invariant, the discrete Euler–Lagrange equations are reduced to the discrete Euler–Poincaré–Suslov equations. The dynamics associated with the discrete Euler–Poincaré–Suslov equations is shown to evolve on a subvariety of the Lie ...

Structural Properties of Inner Amenable Discrete Groups