We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in $v_n$-periodic groups. The case $n=0$ corresponds to rational theory. In analogy with Quillen's results case, we prove this is equivalent Lie algebras $T(n)$-local spectra. also compare it commutative coalgebras spectra, where turns out there only an equivalence up certain convergen...

We construct a numeric algorithm for completing the proof of conjecture asserting that all deformed preprojective algebras generalized Dynkin type are periodic. In particular, we obtain an algorithmic procedure showing non-trivial types E7 and E8 exist only in characteristic 2. As consequence, show E6, periodic classification such algebras, up to algebra isomorphism. do it by reduction solution...

In this paper we develop combinatorial techniques for the case of string algebras with aim to give a characterization complexes infinite minimal projective resolution. These will be called periodic complexes. As consequence characterization, two important applications. The first one, is sufficient condition algebra have global dimension. second exhibit class indecomposable objects in derived ca...

We establish basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds (such as algebras of Bohr’s holomorphic almost periodic functions on tube domains or algebras of all fibrewise bounded holomorphic functions arising, e.g., in the corona problem for H). In particular, in this context we obtain results on holomorphic extension fr...

Cuntz and Quillen have shown that for algebras over a field k with char(k) = 0, periodic cyclic homology may be regarded, in some sense, as the derived functor of (non-commutative) de Rham (co-)homology. The purpose of this paper is to formalize this derived functor analogy. We show that the localization DefPA of the category PA of countable pro-algebras at the class of (infinitesimal) deformat...

Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie algebras beyond Jordan ones may be useful for a description of almost periodic, asymptotically periodic, almost asymptotically periodic, and possibly, more cha...